logic problem solving example

• PRO Courses Guides New Tech Help Pro Expert Videos About wikiHow Pro Upgrade Sign In
• EDIT Edit this Article
• EXPLORE Tech Help Pro About Us Random Article Quizzes Request a New Article Community Dashboard This Or That Game Happiness Hub Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
• Browse Articles
• Learn Something New
• Quizzes Hot
• Happiness Hub
• This Or That Game
• Train Your Brain
• Explore More
• Support wikiHow
• About wikiHow
• Log in / Sign up
• Hobbies and Crafts
• Puzzles and Memory Games
• Mathematical Puzzles

How to Solve Logic Puzzles

Last Updated: October 8, 2023

This article was reviewed by Timothy Huynh . Timothy Huynh is a Rubik’s Cube Artist based in Tampa, Florida. Timothy has been solving Rubik's Cubes professionally since 2016 and became a Guinness World Record Holder with advanced Rubik's cube-solving skills. Timothy has a follower base of over 8.6 million YouTube subscribers and 124k followers on Instagram. Internet celebrities including David Dobrik and Simu Liu have sung his praises, and Pixar has deemed his work "incredible." This article has been viewed 301,568 times.

This article includes general advice for logical reasoning problems, as well as thorough instructions for solving the most common type of logic puzzle. This type of puzzle provides a list or paragraph of clues, then asks you a question that requires you to use the clues to answer. Many books and websites that contain these logic puzzles come with a grid to help you solve them, but this article also includes instructions for making your own.

Setting up a Grid

• Here's an example problem: Three friends named Anna, Brad, and Caroline agree to bring one dessert each to a birthday party. Each friend is wearing a different color shirt. Anna wears a blue shirt. The person who brought brownies couldn't find her red shirt today. Brad didn't bring any dessert at all, which made the person wearing a yellow shirt irritated. Which person brought the ice cream?
• The example question, like all logic puzzles of this type, asks you to match two categories together. You start out knowing the names of several people and the names of several desserts, but you don't know who brought which dessert. Using the clues in the description, you need to figure out how to match each person to a dessert until you know who brought the ice cream. There's actually a third category, shirt color, which should help you get to your answer.
• Note : skip to Using a Grid if the puzzle already comes with a grid set up. Skip to Solving Other Logic Puzzles if your puzzle does not fit this description.

• Write each list separately. When the puzzle mentions a name, add it to a list of names. When the puzzle mentions a color, add it to a separate list of colors.
• Each list should have the same number of items once you've finished. If a list is too short, reread the puzzle carefully for more items.
• Some tricky puzzles will give you hints about what someone doesn't have, such as "Brad didn't make a dessert." In this case, you should add "none" to the list of desserts, which should make it the same length as the other lists.

• For instance, let's say you have three lists. Names : Anna, Brad, Caroline; Desserts : brownies, ice cream, none; and Color of Shirts : red; blue, yellow. Write a vertical list in this order: Anna; Brad; Caroline; (draw a thick line here); brownies; ice cream; none; (draw a thick line here); red; blue; yellow.

• Once you're more familiar with this system, you can get away with not writing every list in both places. We will be using this grid to match items in the vertical list (on the left) to items in the horizontal list (at the top), and sometimes you don't need to match every item. If you've never used this method before, stick with these instructions

• If the list to the left of a section and the list above a section are the same, cross it out. You'll never need to compare the list "Anna, Brad, Caroline" to the list "Anna, Brad, Caroline" – you already know that Anna is Anna.
• Cross out duplicate sections. For instance, the section that compares "Anna, Brad, Caroline" on the left and "red, blue yellow" on the top is the same as the section that compares "red, blue, yellow" on the left and "Anna, Brad, Caroline" on the top. Cross off one of these duplicate sections so you only have one to pay attention to. It doesn't matter which you cross off.

Using a Grid to Solve a Logic Puzzle

• Occasionally, a puzzle cannot be fully solved, meaning you won't be able to fill the entire grid. You should still be able to answer the question it asks.

• If you can't find that square, search the other way around. For instance, find the row labeled "blue" and the column labeled "Anna", instead of the other way around.
• Don't start with a clue that tells you something that doesn't apply, such as "Anna doesn't wear a red shirt." While that's a useful clue that should be marked with an "X", this method will assume you started with a clue that gives positive information.

• In our example, the section that has the clue you just circled compares the names of people to the colors of their shirts. The squares we're crossing off are the combinations we've ruled out, which include Brad or Caroline wearing a blue shirt, and Anna wearing a red or yellow shirt. (Typically, the introduction will tell you that each item can only be matched to one item in each other category.)

• If your puzzle gives you clues about what doesn't match, such as "Anna doesn't wear a red shirt", you should put an X in that column. However, since you haven't found a positive match, you should not cross out any other squares.

• Brad did not bring a dessert. Put a circle in the Brad-none square.
• The person wearing a yellow shirt is not Brad. Put an X in the Brad-yellow square.

• If you're solving a puzzle from another country, look up the names to find out whether they are male or female. Puzzle books that are printed more than 20 years ago will sometimes contain names that were once female, but have now become male (or vice versa).

• The green house comes before another house, so it can't be the last one.
• The black house comes after another house, so it can't be the first one.

• Marcus can't be the one who ran the mile in 6 minutes, no one was ahead of him. Cross out the Marcus-6 square.
• Marcus can't be the one who ran in 8 minutes, because that time is less than 5 minutes behind the one before it. Cross out the Marcus-8 square.
• Either the 15 or 25 minute times would work for this clue. You'll have to wait until more squares are crossed off before you can figure out which time was Marcus's.

• Let's say you've discovered that Caroline wears a yellow shirt. Check the yellow shirt column or row for information in other sections.
• Let's say you notice on your chart that the person with a yellow shirt did not bring ice cream. Because you know that person is Caroline, you can also cross out the square that connects Caroline and ice cream.
• Check Caroline's row or column too and transfer information the same way to the yellow shirt column or row.

• If a row or column within a section has every square crossed off, or more than one square with a circle in it, there was probably a mistake made along the way and you may need to start over.

• If an inconsistency occurs, your guess must have been wrong. Go back to what the chart looked like before you made your guess, and make the opposite one. Always keep track of when you made your guess with a new copy or a different color ink so it's easy to reverse if the guess was wrong.

• If you got the answer without filling out your entire chart, you may not be able to check every clue. As long as your chart doesn't contradict the clues you can check, you are probably correct.

Answering Logical Reasoning Problems

• For example: "A cell phone has fallen down a one foot (30cm) hole. How do you retrieve it? You have a wheel of cheese, three chicken feathers, and a flute." The question is designed to get you thinking about how to use bizarre objects in a creative way, but consider each word and you'll notice the hole is shallow enough to reach down and pick up the cell phone.

• For instance, "A wind is blowing from the east, but you are facing the south side of a tree. Which way are the leaves blowing?" If you don't stop to think, you might have heard "east wind" and automatically answer "east". However, the wind is blowing from the east, so the leaves are actually blowing west.

• For timed tests, if you cannot narrow it down to exactly one answer (or however many the instructions request), you may need to take a guess and move on. Make a note on your notepaper to go back to that question at the end if you have time.

• There are many practice tests available online for free for any major standardized school exam. If you can't find your exact exam, search for practice logic tests that match your education level.

• If the question doesn't give you enough information, make an assumption or estimate and state it clearly. For instance, say "Let's say the skyscraper is 100 stories tall and has 20 windows on each story" or "First, I'll assume everyone is following the speed limit, and then I'll consider what changes if some people are traveling faster."

Expert Q&A

Things You'll Need

• Graph paper
• For difficult puzzles, keep track of which clue you used by putting the number of the clue in your grid instead of a circle. You may need to add numbers to each sentence of the puzzle description first if the clues do not come in a numbered list. Thanks Helpful 0 Not Helpful 0
• Some people prefer to keep the duplicate sections when setting up a graph, while others dislike having to keep the same information in two places. Thanks Helpful 0 Not Helpful 0
• If you have a spreadsheet program on your computer, you can set up your grid there using the border tool to outline the cells. Then, if you have to choose between two answers (see Step 13), you can simply copy and paste the entire 'solution so far' to another section of the spreadsheet to prove or disprove your guess. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ http://www.psychometricinstitute.com.au/Psychometric-Guide/Logical-Reasoning-test.html

About This Article

To solve logic puzzles, start by rewriting the question to eliminate any unnecessary or nonsensical information. Then, make a list of important clues, such as colors, names, and words that indicate a particular order, like “before” and “after.” If the puzzle is a multiple choice question, check each answer to see if it contradicts something in the question, or if the answer can’t be deduced from the given information. Afterwards, if you’re still stuck, reread the puzzle to see if you’ve missed any clues. To learn more, including how to solve logic puzzles using a grid, scroll down. Did this summary help you? Yes No

• Send fan mail to authors

Did this article help you?

Featured Articles

Trending Articles

Watch Articles

• Terms of Use
• Privacy Policy
• Do Not Sell or Share My Info
• Not Selling Info

Don’t miss out! Sign up for

wikiHow’s newsletter

Logic Problems

Why logic problems.

A logic problem is a general term for a type of puzzle that is solved through deduction. Given a limited set of truths and a question, we step through the different scenarios until an answer is found. While these problems rarely involving coding, they require problem-solving and the ability to articulate plausible outcomes.

You may encounter logic problems during technical interviews for a programming position so it’s worth developing a strategy on how to approach these questions. They’re also a fun way to strengthen your algorithmic reasoning skills!

Our Question: Apples, Oranges, or Both?

We’ll start with the following problem. You’re faced with three jars labeled “Apples”, “Oranges”, and “Both”. You cannot see the contents of these jars, but you’re informed that each is mislabeled . The contents of the jar are not decribed by the label.

How many times would you need to draw from a jar in order to accurately label each jar?

Our Solution: Using the Information

Let’s boil down our problem into factual statements we can use to draw conclusions.

• The jars are mislabeled
• There are three jars
• One jar is a combination of the contents of the other two jars.

We can use these facts to deduce further information which will be instrumental in solving the problem.

First we can rephrase “the jars are mislabeled” as “the jar labeled ‘Apples’ does not contain Apples “. It’s the same information but presented in a way that will be easier to work towards a solution.

We should also be drawn to item 3: there’s more information available in the “Both” jar which makes it a more “fruitful” source of inquiry. In general, be aware of any exceptions or abnormalities in the phrasing of the question.

Our Solution: Filling in Scenarios

Now we’ll begin walking through hypothetical situations. Being able to reason through the problem and articulate your thought process is essential to performing well in a technical interview.

Let’s imagine we draw a fruit from the jar labeled “Apples”. We know this jar doesn’t only contain apples, but we’re faced with two possibilities. We could draw an apple or we could draw an orange. If we drew an apple, we’d know this was the “Both” jar, but what if we drew an orange? Then this jar remains a mystery, either “Both” and we just happened to draw an orange, or it’s purely “Oranges”. We’re still in the dark!

The thought process is the same for drawing from the “Oranges” jar, so now imagine drawing from the “Both” jar. Again, we may draw either type of fruit, but we’ve learned something more substantial. If we draw an orange, we know this is “Oranges”. If we draw an apple, we know this is “Apples”. There is no ambiguity because the jar is mislabeled as “Both”.

Our Solution: Drawing Conclusions

We’ve identified one jar, do we need to make additional queries? We should return to our Use the Information step. Let’s say we’ve identified “Oranges”.

We have the old “Both” jar, now correctly labeled “Oranges”, and two mislabeled jars: “Oranges” and “Apples”. Can we draw further conclusions? We can!

“Apples” and “Oranges” are both mislabeled, but we have new information. We know where the true “Oranges” is. This doesn’t help us with the mislabeled “Oranges”, it could be either “Both” or “Apples”.

It does help with “Apples”. We know “Apples” is not “Oranges” because we’ve already identified “Oranges”. We also know “Apples” isn’t really “Apples” because it’s mislabeled. That leaves only one option, this jar is “Both”.

With two correctly labeled jars, the third is easily identified as “Apples”

To wrap it up: “Both” –> “Oranges”, which leads us to “Apples” –> “Both” and “Oranges” –> “Apples”

Practice Makes Perfect!

We’ll finish this article with a few practice problems for you to try on your own. Each problem has a link which will take you to an explanation of the solution.

Knights and Knaves

“Knights and knaves” are a popular type of logic puzzle that involves an island inhabited by two types of people: knights and knaves.

• Knights always tell the truth
• Knaves always lie

On the island, you encounter three people, Ted, Ben and Lil.

Ted says, “at least one of the following is true, that Lil is a knave or that I am a knight.”

Ben says, “Ted could claim that I am a knave.”

Lil says, “neither Ted nor Ben are knights.”

Who is a knight and who is a knave?

Here’s the solution.

Three Fastest Horses

We’d like to find the three fastest horses from a group of 25.

We have no stopwatch and our race track has only 5 lanes. No more than 5 horses can be raced at once.

How many races are necessary to evaluate the 3 fastest horses?

'The Codecademy Team, composed of experienced educators and tech experts, is dedicated to making tech skills accessible to all. We empower learners worldwide with expert-reviewed content that develops and enhances the technical skills needed to advance and succeed in their careers.'

Related articles

From editor to output, how to enroll in the apple developer program, learn more on codecademy, code foundations, full-stack engineer.

• IBPS RRB Exam 2023 - Free Course
• Current Affairs
• General Knowledge
• SSC CGL Pre.Yrs.Papers
• SSC CGL Practice Papers
• SBI Clerk PYQ
• IBPS PO PYQ
• IBPS Clerk PYQ
• SBI PO Practice Paper

Logical Problems in Logical Reasoning

Logical Problems in Reasoning: Logical Problems are like captivating puzzles and challenges that test your thinking skills. These Logical problems questions present complex scenarios where you need to find patterns, make logical connections, and come up with precise solutions. Logical Problems come in various forms, from math puzzles that require number skills to creative challenges where you need to think outside the box. They are a great way to improve your critical thinking, boost your brainpower, get better at solving real-life problems and become more efficient at resolving real-life problems through the application of logical reasoning .

In this article, we will provide you with a variety of logical problems and answers. We will also discuss some common strategies for solving logical problems and its explanation as well for better understanding.

Logical Problems with Answers – Solved Examples

Solved Example 1:

Tanya is older than Eric.

Cliff is older than Tanya.

Eric is older than Cliff.

If the first two statements are true, the third statement is

c. uncertain

Answer: b. false

Explanation: If Tanya is older than Eric, and Cliff is older than Tanya, it implies that Eric is younger than Cliff, contradicting the third statement. Therefore, the third statement is false.

Solved Example 2:

In a row of cars, Tina’s car is red.

John’s car is behind Tina’s car.

Katie’s car is in front of John’s car.

Answer: a. true

Explanation: If Tina’s car is red, and John’s car is behind Tina’s car, it implies that Katie’s car must be in front of both Tina’s and John’s cars for the statements to be true. Therefore, the third statement is true.

Solved Example 3:

All apples in the basket are green.

Some fruits in the basket are apples.

Therefore, some fruits in the basket are green.

Explanation: If all apples in the basket are green, and some fruits in the basket are apples, it logically follows that some fruits in the basket are green. Therefore, the third statement is true.

Solved Example 4:

All students in the class passed the math exam.

Some students in the class failed the science exam.

Therefore, some students in the class failed at least one exam.

Explanation: If all students in the class passed the math exam, and some students in the class failed the science exam, it logically follows that some students in the class failed at least one exam. Therefore, the third statement is true.

Solved Example 5:

John is taller than Alice.

Alice is taller than Bob.

Therefore, John is taller than Bob.

Explanation: If John is taller than Alice, and Alice is taller than Bob, it logically follows that John is taller than Bob. Therefore, the third statement is true.

Solved Example 6:

All triangles have three sides.

This shape has three sides.

Therefore, this shape is a triangle.

Explanation: If all triangles have three sides, and this shape has three sides, it logically follows that this shape is a triangle. Therefore, the third statement is true.

Solved Example 7:

All dogs are mammals.

Some animals in the zoo are dogs.

Therefore, some animals in the zoo are mammals.

Explanation: If all dogs are mammals, and some animals in the zoo are dogs, it logically follows that some animals in the zoo are mammals. Therefore, the third statement is true.

Solved Example 8:

All birds have feathers.

This animal has feathers.

Therefore, this animal is a bird.

Explanation: If all birds have feathers, and this animal has feathers, it logically follows that this animal is a bird. Therefore, the third statement is true.

Solved Example 9:

Some fruits are sweet.

All apples are fruits.

Therefore, some apples are sweet.

Explanation: If some fruits are sweet, and all apples are fruits, it logically follows that some apples are sweet. Therefore, the third statement is true.

Solved Example 10:

All cars have wheels.

Some vehicles have wheels.

Therefore, some vehicles are cars.

Answer: c. uncertain

Explanation: While all cars have wheels, and some vehicles have wheels, it does not necessarily mean that some vehicles are cars. The term “vehicles” is more inclusive and can refer to various types of vehicles, not just cars. Therefore, the third statement is uncertain.

Related Resource :

• Essential Part – Logical Reasoning​​
• ​ Artificial Language – Logical Reasoning​
• ​Matching Definitions – Logical Reasoning

Please Login to comment...

Similar reads.

• SSC/Banking
• Banking Quantitative Aptitude
• Logical Reasoning
• SSC Quantitative Aptitude
• How to Underline in Discord
• How to Block Someone on Discord
• How to Report Someone on Discord
• How to add Bots to Discord Servers
• GeeksforGeeks Practice - Leading Online Coding Platform

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Origami-engineered tubes weigh 2 lbs, hold 165 pounds, fold flat for easy use

Japan scrambles fighter jets, fires flares at russian spy aircraft in a first, 1 in 10 billion: cern’s breakthrough kaon decay discovery sparks new physics, scientists simulate nuclear strikes in lab to deflect dinosaur-killing asteroids.

21 hours ago

China unveils 90 mph kamikaze drone threatening Taiwan with 124-mile range

Ford patents drug trafficking tech to save drivers from becoming ‘blind mules’ .

20 hours ago

220kW force: HORSE kicks off production of powerful 1.2L hybrid turbo engines

19 hours ago

Elon Musk’s wish fulfilled as Olympic shooter Kim Yeji takes on assassin role 

Nasa to shoot spectrometer ‘bullet’ into moon, mars surfaces to study composition, ‘killer whale holding a knife’: ai uncovers 303 unique nazca lines in peru's desert, ‘suicide capsule’ death in swiss forest prompts multiple arrests, legal probe  .

26 minutes ago

New nasal spray offers 99.99% protection against flu, pneumonia, COVID-19

an hour ago

Scientists spin strong spider silk to heal diabetes wounds, repair joints

2 hours ago

The AI Wild West: Will California rein in big tech with SB 1047?

15 hours ago

UM325: Transformer-like electric spider crane can lift 7,120 pounds silently

17 hours ago

Georgia Tech's iron cathode could slash EV battery costs, boost efficiency

Months to days: co2 laser crafts centuries-old thai royal umbrellas in 113 hrs.

18 hours ago

‘World first’: France uses space lasers to communicate with satellite from ground

Donald trump or kamala harris monkeys predict us presidential election outcome, hidden in magma: ancient volcanoes hold rare metals used in phones and tvs , 9 tricky logic puzzles to test your problem solving skills, make your brain earn its keep with these hard puzzles..

Christopher McFadden

1 ,  2

Would you like to exercise your brain today? Then, here are 9 tricky puzzles to give your grey-matter a good workout .

We have provided the solutions as links at the end of each puzzle below, in case you want to have a go before checking your answers. Enjoy, and good luck!

What are some difficult logical puzzles that will sharpen your mind?

So, without further ado, here are some examples of difficult puzzles that will certainly hone your mental acuity. Trust us when we say this list is far from exhaustive and is in no particular order.

1. The riddle of the farmer

IntangibleArts/Flickr

This first puzzle is a bit of a classic. Just suppose you had a farmer who needs to transport a fox, a chicken, and some corn across a river.

He only has a small boat that can only carry him and one of them with him per crossing. The farmer needs to get all three items across the river in one piece.

But there is a problem. He can’t leave the fox and chicken alone as the fox will eat the chicken. Likewise, he can’t leave the chicken with the corn as the chicken will munch down on the corn.

So, can you figure out how the farmer could solve this problem?

Here is the solution if you want to test your workings. 

2. The rope bridge at night problem

Frerk Meyer/Flickr

This next puzzle is another head-scratcher. Suppose there are four people trying to cross a rather dodgy rope bridge in the middle of the night.

Only two of them can cross it at a time and they only have a single flashlight between them. For this reason, one person of each pair must return to help the others get across.

But time is limited; they are being chased and need to get across within 17 minutes total. Sounds simple enough, except each person can only cross the bridge at a certain rate.

One person takes 1 minute to cross the bridge. The second takes 2 minutes , the third 5 , and the last person 10 minutes .

Each pair can only cross as fast as the slowest member of the pair. How can they all cross the bridge in time?

Here is the solution if you want to see if you were right. 

3. The burning rope timer problem

WildInWoods/Flickr

Let’s suppose you needed to measure a time of exactly 45 minutes but only had a couple of old ropes coated in oil and a lighter. You know that each rope takes exactly 1 hour to burn all the way through.

But the ropes do not burn at a uniform rate with spots that will burn a little faster than others. Whatever the case, and location of these slow and fast burn spots, the entire rope still burns up in exactly an hour.

You can burn the ropes at either end or at multiple points at the same time. How would you measure exactly three-quarters of an hour?

Here is the solution . 

4. The heads or tails coin problem

William Warby/Flickr

Just suppose you are sitting at a table strewn with hundreds or thousands of coins . You are blindfolded, so you cannot see the coins, and you don’t know how many there are.

You are told that 20 of the coins are tails-side up while the rest are heads up. You can move the coins and flip them over as much as you want but you will never be able to see what you doing. 

While you can feel the coins, you are unable to determine which side is which. 

How then, would you separate the coins into two piles that have the same number of tails-side-up coins? Remember the number of coins per pile does not need to be the same. 

Here is the solution , if you are curious. 

5. The classic water jug problem

Dwight Sipler/Flickr

Here is another classic puzzle that will sharpen your mind. Let’s suppose you need to measure out exactly 4 liters of water.

But, of course, you have a problem. You have two containers each 3 and 5 liters in volume respectively. 

Each container has no other marking except for the fact that it only provides its known volume. Using a running tap to fill them how would you measure out exactly 4 liters ?

Here is the solution , if you want to check your answer.

6. The riddle of the Gods

roadscum/Flickr

Touted as one of the hardest puzzles to solve ever , this one is certainly a fun challenge. Let’s suppose we have three gods called, in no particular order, “True”, “False” and “Random”.

We don’t know which is which, so, for now, we will label them A, B, and C respectively.

“True” always tells the truth. “False” always lies, and “Random” lies or tells the truth at random.

You are tasked with identifying which one is which by asking three yes-no questions. Also, you can only ask one god one question at any one time.

But it’s a little more complex than that. Each god understands English but will only answer in their own language as “da” or “ja” — but you can’t understand if the answers are in the affirmative or not.

How would you solve this? Here is the solution . 

7. Escape from the field

halfshutter/Flickr

Let’s suppose you have been placed in a circular field of unknown radius R. The field has a low fence around it.

Attached to the wire fence is a large, angry, sharp-fanged and hungry dog who loves nothing more than eating human flesh. You can run at a speed v, while the dog can run exactly 4-times as fast as you.

The dog, as it is attached to the fence can only travel around the perimeter. How would you escape from the field in one piece?

8. The apples and oranges puzzle

WriterGal39/Flickr

Here is another annoying problem that needs solving . Let’s suppose you work in a fruit factory that boxes apples and oranges. 

One day, the labeling machine goes haywire and incorrectly labels the crates of fruit. Your coworker decides to have a bit of fun and pulls out three crates of fruit and tells you that one has just oranges in it, the second just apples, and the third a mixture of the two.

One of the crates is labeled “O” for oranges, another “A” for apples, and the third “A+O” for apples and oranges. But the labels lie.

You can pick one crate and your coworker will pull a single fruit from it to show you. You are only able to do this once. 

How can you figure out which crate actually has only oranges, only apples, and a mixture of the two? Here is the solution . 

RECOMMENDED ARTICLES

9. the mystery hat puzzle.

Neil Moralee/Flickr

And finally, let’s suppose you have a dark closet with five hats in it. There are three blue, and two red ones. 

Three men go into the closet and each selects a hat at random in the dark and places it on their head. Once outside the closet, each man is unable to tell what color their own hat is. 

The first man looks at the others and says “I cannot tell what color my hat is!”. The second hears this, looks at the other two, and declares “I cannot tell what color my hat is either!”.

The third man, who is blind, confidently declares “I know exactly what color mine is!”. 

What color is his hat? Here is the solution .

The Blueprint Daily

Stay up-to-date on engineering, tech, space, and science news with The Blueprint.

By clicking sign up, you confirm that you accept this site's Terms of Use and Privacy Policy

ABOUT THE EDITOR

Christopher McFadden Christopher graduated from Cardiff University in 2004 with a Masters Degree in Geology. Since then, he has worked exclusively within the Built Environment, Occupational Health and Safety and Environmental Consultancy industries. He is a qualified and accredited Energy Consultant, Green Deal Assessor and Practitioner member of IEMA. Chris’s main interests range from Science and Engineering, Military and Ancient History to Politics and Philosophy.

POPULAR ARTICLES

Space makes heart tissues age 5x faster, slows heartbeat, finds shocking study, made-to-order homes, related articles.

New revolutionary fireproof fabric for EV batteries can withstand 2,300°F heat

AmpAura’s “Bust the Fumes” campaign: Tech enthusiasts smash gas generators to embrace solar power

‘Killer whale holding a knife’: AI uncovers 303 unique Nazca lines in Peru’s desert

Reset password New user? Sign up

Existing user? Log in

Solving Propositional Logic Word Problem

Already have an account? Log in here.

Recommended Course

Stretch your analytic muscles with truth-tellers, liars, logical robots, and more!

• Chris Hambacher
• Pranshu Gaba
• Shreyansh Singh Solanki
• Rafael Macedo
• Andrew Ellinor
• Mahindra Jain
• Pedro Teixeira
• Suyeon Khim

Propositional logic is a formal language that treats propositions as atomic units. A typical propositional logic word problem is as follows:

A, B, C, D are quarreling quadruplets. If A goes to the party, then B will not go. If C goes to the party, then B will not go. What is the largest possible number that will go to the party?

Logic is the study of valid reasoning. It is applied not only in studies but also in our day-to-day lives. Using simple logical reasoning and deduction, we are able to obtain information from a certain premise. Likewise, we can also verify or disprove statements.

We will be discussing ways of identifying common mistakes and how to avoid them. We will also talk about different proof techniques, such as using Venn diagrams and analogies so that you have a toolkit for solving logic word problems.

What's wrong with this proof?

Proof by venn diagram, proof by analogy.

In this section, we will use familiar notations used in propositional logic. You might want to familiarize yourself with Propositional Logic first.

Like solving any other questions, we should always ask ourselves what we can and can't do when writing out our reasoning. The first step to learn how to solve propositional logic problems is to list out what can't be done or what is not a possibility so we can narrow down what the possible scenarios are. Remember that it is very easy to fall into an erroneous conclusion based on faulty reasoning. Take the statements below as an example, if the first statement is true, is the second statement also true?

\[\begin{array} &\text{"If it's raining, then I can't play soccer".} &\text{"If I can't play soccer, then it's raining."} \end{array}\]

It is pretty clear that the issue here is: there can be other reasons why I can't play soccer, which doesn't necessarily depend on the weather. If we make such simple errors in reasoning when the context is very clear, just imagine what will happen when you are less certain about statements that are more vague. In the next paragraph, we will be introduced to these errors.

Converse and Inverse Errors

As a beginner, the most common mistake you can make is to assume that the converse and/or inverse of the original statement is also true. Take a look at the two sections below:

Introduction to Converse Error with erroneous reasoning:

Premise : If it's raining, then I can't play soccer. Conclusion : If I can't play soccer, then it's raining. Explanation : From the first statement, we are given a condition and a result: "raining" as a condition and "I can't play soccer" as a result. The entire premise is phrased in such a way that if the condition is fulfilled, then the result will occur. However, the conclusion shows that if the result is fulfilled, then the condition will occur. This does not make sense because it is not necessary for the condition to take place if the result occurs first. This is known as a converse error. In a general form, the argument for a converse error is as follows: If P occurs, then Q occurs. Q occurs. Therefore, P also occurs.

Introduction to Inverse Error with erroneous reasoning:

Premise : If it's raining, then I can't play soccer. Conclusion : If it's not raining, then I can play soccer. Explanation : From the first statement, we are given a condition and a result: "raining" as a condition and "I can't play soccer" as a result. The entire premise is phrased in such a way that if the condition is fulfilled, then the result will occur. However, the conclusion shows that if the condition does not occur, then the result does not occur either. This does not make sense because there can be other reasons/factors such that the result does occur. This is known as an inverse error. In a general form, the argument for an inverse error is as follows: If P occurs, then Q occurs. P does not occur. Therefore, Q also does not occur.

It may now be abundantly clear that it is easy to identify we've made an erroneous reasoning. However, what if the statements given appear more vague? This is the reason why we introduce the two errors above (converse error and inverse error) to show that not all wrong statements are easily identifiable. Simply put, the relationship between two events do not necessarily imply that one causes the other. In short, we are pointing out the common fact that "correlation does not imply causation".

Now that we have seen these mistakes first hand, let's do another example to remind ourselves that they are mistakes and we can hopefully avoid them in the future. Keep in mind that some of the converse/inverse statements can appear ridiculous but some do not.

We are given the following statement: If today is Sunday, then the weather is sunny. \[\] \(\qquad \text{ (i)}\) Write the inverse and converse of this statement. \(\qquad \text{(ii)}\) Identify which of these statements you have made is not logical and explain why. \(\text{(i)}\) Inverse and Converse Inverse: If today is not Sunday, then the weather is not sunny. Converse: If the weather is sunny, then today is Sunday. \(\text{(ii)}\) Logical or Illogical Though they are the inverse and converse of the original statement, we must keep in mind that they might not necessarily be an error. However, there is no harm in checking whether they are correct or not. The inverse statement implies that the day has a direct relation on the weather being sunny or not, which is ludicrous because there can also be non-sunny days which do not fall on a Sunday. The converse statement implies that only if the weather is sunny then the day is Sunday, which is also ludicrous because they can also have a sunny weather on days not falling on a Sunday. \(_\square\)

Pinpoint the exact error

Now that we can identify how the errors occur, let's take a step further and apply these techniques so that we can pinpoint exactly where the error occurs. Note that the easiest way to identify where the error arose is to convert logical statements into symbolic forms (like P implies Q). Let's try the following example.

Taking the long view on your education, you go to the Prestige Corporation and ask what you should do in college to be hired when you graduate. The personnel director replies that you will be hired only if you major in mathematics or computer science, get a \(\text{B}^\text{+}\) average or better, and take accounting. You do, in fact, become a math major, get a \(\text{B}\) average and take accounting. You return to Prestige Corporation, make a formal application, and are turned down. Did the personnel lie to you? Let's list down the requirements to be hired: \(\begin{array}{r r l} & \text{(i)} & \text{Major in mathematics or computer science}\\ & \text{(ii)} & \text{Get a } \text{B}^\text{+} \text{ average or better}\\ & \text{(iii)} & \text{Take accounting}\\ \end{array}\) Since you became a math major, criteria \(\text{(i)}\) is satisfied. Since you got a \(\text{B}\) average instead of a \(\text{B}^\text{+}\) average, criteria \(\text{(ii)}\) is not satisfied. Since you took accounting, criteria \(\text{(iii)}\) is satisfied. Since you did not satisfy all the criteria and were turned down, the personnel didn't lie to you. \(_\square\)

Now that you're familiar with writing out these statements and identifying possible errors, let's try another example that uses such a property!

A store has been raided by looter/s, who drove away in a car. Three well-known criminals Satvik, Krishna and Sharky are brought to the police station for questioning. Inspector Aditya of the police extracts the following facts:

\((1)\) None other than Satvik, Krishna and Sharky was involved in the robbery. \((2)\) Sharky never does a job without using Satvik (and possibly others) as accomplices. \((3)\) Krishna doesn't know how to drive.

Find the person who, in any case, is guilty.

This problem is the part of my set "Is This What You Call Logic?"

Formal terminologies.

In the previous sections, we have learned the two most common errors that students will make when solving a logical reasoning problem. However, we did not formally touch on the terminologies for those terms: converse error and inverse error. Let's begin!

Contrapositive : A statement is logically equivalent to its contrapositive. The contrapositive negates both terms in an implication and switches their positions. For example, the contrapositive of "P implies Q" is the negation of Q implies the negation of P.

Converse : The converse switches the positions of the terms. The converse of "P implies Q" is "Q implies P".

"If and only if", sometimes written as iff and known as equivalence, is implication that works in both directions. "P if and only if Q" means that both "P implies Q" and "Q implies P".

Let's try a few examples that cover this area!

\(\text{ (i)}\) Write down the contrapositive statement for \[\text{"If you are human, then you have DNA."}\] \(\text{(ii)}\) Write down the two if-then statements for \[\text{"A polygon is a quadrilateral if and only if the polygon has 4 sides."}\] \(\text{ (i)}\) contrapositive \(\qquad\) If you do not have DNA, then you are not human. \(\text{(ii)}\) if-then statements \(\qquad\) If a polygon is a quadrilateral, then it has 4 sides. \(\qquad\) If a polygon has 4 sides, then it is a quadrilateral. \(_\square\)

Simple, isn't it? Let's try some problems that apply the techniques we have learned above.

If Jeff spends 5 hours playing video games, then he cannot finish his math homework.

If Jeff finishes his math homework, then he will do well on his next math test.

Based on this information, which of the following is logically correct?

Selena, Jennifer and Miley wear a blue dress, yellow dress, and green dress in an unknown order. It is known that:

1) If Selena wears blue, then Jennifer wears green. 2) If Selena wears yellow, then Miley wears green. 3) If Jennifer does not wear yellow, then Miley wears blue.

What is the color of the dress Selena is wearing?

Now that we have mastered these techniques, let's move on to the following section for other cool proof techniques!

In this section, we will be applying some basic rules of set notations. You might want to familiarize yourself with sets and Venn diagram first.

In the previous section, we have learned the most common ways in identifying and pinpointing errors. In this section, we will apply the use of Venn Diagram as an alternative proof in solving logical reasoning problems. But what's the benefit of this? Well, it's simple: We do not need to verbalize these statements and we can use the visual aids to guide us to solve these problems.

Recap of set notations and Venn diagram \[\]

Let's do a brief recap for the application of Venn Diagrams by taking the following as an explicit example:

Consider \(W,X,Y,Z\) as sets, each with their own elements in them. Then by interpreting the Venn Diagram, we can obtain information like:

• All elements in set \(W\) is in set \(Y\).
• All elements in set \(X\) is in set \(Z\).
• Not all elements in set \(Y\) is in set \(W\).

How to use Venn diagrams to solve a logical word problem \[\]

Let us consider the following statements and deduce whether the conclusion is true or false by Venn diagram:

True or false? \[\] It is given that all birds have wings. All chickens are birds. Therefore, all chickens have wings. Explanation : By Venn diagram, the statement "A chicken is a bird." implies that the set "all chickens" is a subset of "all birds." Thus we can say that all chickens have the same characteristics as a bird. Because it is given that all birds have wings (a characteristic), all chickens have wings too. Thus the conclusion is correct. Note : We should keep in mind that this only works if the premise is true. For example, if we replace the word "wings" by "forearms" in the first statement, then the conclusion of "All chickens have forearms." will inevitably be true despite its ridiculous claim.

Food for thought : If all phones have batteries and I have a phone, does it mean that my phone has a battery?

Careful! There are other ways of drawing out Venn diagrams!

Though it may appear very simple to set up a Venn diagram, the setup may not necessarily be unique. Let us consider a revised version of the statements above and deduce whether the conclusion is true or false by Venn diagram.

True or false? \[\] It is given that all birds have wings. All chickens are birds. Therefore, all birds are chickens. Explanation : By Venn diagram, the statement "A chicken is a bird" implies that the set "all chickens" is a subset of "all birds." Thus we can say that all chickens have the same characteristics as a bird. However, it is not necessarily true that all birds share the same characteristics of a chicken. (Sounds familiar? It's converse error.) So the claim "All birds are chicken" must be false. Note : To fix the conclusion, you should say " Some birds are chickens" instead of " All birds are chickens."

Now that we know the fundamental applications of proof by Venn diagram, let's apply these knowledge we learned on the following examples:

True or False?

\(\quad\) All pangs are pings. \(\quad\) Some pings are pongs. \(\quad\) Therefore, some pangs are pongs.

Johannes has several written publications on his bookshelf. Albert notices that all of the comics are paperback books, and that some of the paperback books are manga. Are all comics manga?

Image Credit : Wikimedia Johannes Jansson

Isn't the proof by Venn diagram fun? You don't need to use actual words to formalize these statements. Looks very unusual, right? But it works. Speaking of unusual, is it possible to solve these logical statements if we were to spice things up by dramatizing out the statements? Yes, we can! Proof by analogy is another proof technique to solve logical problems. See the following section:

How do we solve texts that are seemingly hard to decipher?

All pangs are pings. Some pings are pongs. Therefore some pangs are pongs.

Consider the logical statements given above. Since we can't relate to or identify what pangs, pings, or pongs are, it will appear that these terms are vague or all too similar. How are we supposed to solve problems like this if we have little to no clue to what is going on? Well, proof by analogy will be useful here: this is when we dramatize or caricaturize the terms used.

For example, we may call pangs as humans, pings as apes, and pongs as gorillas. With these new terms, we are able to visualize what they are. Rewriting them into the original 3 statements shows that

\[\text{All humans are apes. Some apes are gorillas. Therefore some humans are gorillas.}\]

So the given conclusion is wrong because of the ridiculousness of the conclusion "Some humans are gorillas."

However, an important question to ask is why this works. This is too good to be true, right? Or, are we running into some wrong argument? Why does this work?

Explanation of how this works

The reason why proof by analogy works is because we make an inference that if the objects have multiple similar characteristics, and it is given that you know one of them have an extra characteristics (call it X), then it is not a bad inference to conclude that the other object shares that same characteristic X.

To put it short, the generalized/structured form for proof by analogy is:

P and Q has similar properties \(x_1, x_2, x_3, \ldots, x_n\). We know that P has a further property \(y\). Therefore, Q probably has property \(y\) too.

Now let's try a modified version of the ping-pang-pong question from earlier!

True or false? \[\] \(\qquad\) All yangs are yengs and yings. \(\qquad\) Some yengs are yings. \(\qquad\) Then, all yengs are yangs. This is false. Let "yangs" be defined as "pets", "yengs" as "tigers", and "yings" as "cats". So it is true (or at least still reasonable) that all pets are cats and tigers and that some tigers are cats. But it is not true that all tigers are pets. \(_\square\) Note: The reason why proof by analogy works best here is because we couldn't label or identify any characteristics for yangs, yengs, and yings. Therefore, a sensible approach is to prove by analogy.

Now that you're ready to solve logical problems by analogy, let's try to solve the following problem again, but this time by analogy!

Suitability of analogy

Notice from the previous section that we've mentioned that "Q probably has property \(y\) too." instead of "Q definitely has a property \(y\) too." This is because the argument may provide what appears to be the right evidence, but the conclusion does not always follow. This subsection explains why this proof (arguemnt) might not always work.

Though it is true that we highlight or amplify parallel characteristics, the differences between things can often overwhelm their similiarities. One might note that it is always possible to extend an analogy to the point of absurdity. For illustration, take the following famous "Information Argument":

DNA is a code. A code requires an intelligence. Therefore, DNA comes from an intelligence.

Yes, this will sound completely logical if we apply the implications approach. That is, it's P implies Q and Q implies R, so P implies R. However, the argument here is not valid because the statement "DNA is a code." is purely an analogy and thus it is not an entirely accurate statement to begin with. Thus, we have started with a wrong premise. So the merits of analogy do not hold. This is further explained in Analyzing arguments from analogy .

We can see that proof by analogy is very useful and can also be used to make incorrect conclusions. Thus, one must be careful in labeling certain characteristics when using this method. Let's see the following examples to see how the proof by analogy backfires:

True or false? \[\] All squares and rectangless are convex, have four sides and form right angles at their vertices. All squares have sides of the same length. Therefore, all rectangles have sides of the same length. This is obviously false because by definition, all rectangles do not have sides of the same length, but only squares have sides of the same length. We make the wrong conclusion that rectangles also have this characteristic because it is known previously that both share a number of characteristics. \(_\square\)

True or false?

It is given that Amy, Bernadette and Penny are good friends of Sheldon and Leonard.

Leslie is a good friend of Leonard.

Therefore, Leslie is a friend of Sheldon as well.

Image Credit: Wikimedia TBBT. No copyright infringement intended.

• Propositional Logic Using Algebra .
• Propositional Logic .
• Truth-tellers and Liars .
• Logic gates .

Master concepts like these

Learn more in our Logic course, built by experts for you.

Problem Loading...

Note Loading...

Set Loading...

26 Expert-Backed Problem Solving Examples – Interview Answers

Published: February 13, 2023

Interview Questions and Answers

Actionable advice from real experts:

Biron Clark

Former Recruiter

Contributor

Dr. Kyle Elliott

Career Coach

Hayley Jukes

Editor-in-Chief

Biron Clark , Former Recruiter

Kyle Elliott , Career Coach

Hayley Jukes , Editor

As a recruiter , I know employers like to hire people who can solve problems and work well under pressure.

 A job rarely goes 100% according to plan, so hiring managers are more likely to hire you if you seem like you can handle unexpected challenges while staying calm and logical.

But how do they measure this?

Hiring managers will ask you interview questions about your problem-solving skills, and they might also look for examples of problem-solving on your resume and cover letter. 

In this article, I’m going to share a list of problem-solving examples and sample interview answers to questions like, “Give an example of a time you used logic to solve a problem?” and “Describe a time when you had to solve a problem without managerial input. How did you handle it, and what was the result?”

• Problem-solving involves identifying, prioritizing, analyzing, and solving problems using a variety of skills like critical thinking, creativity, decision making, and communication.
• Describe the Situation, Task, Action, and Result ( STAR method ) when discussing your problem-solving experiences.
• Tailor your interview answer with the specific skills and qualifications outlined in the job description.
• Provide numerical data or metrics to demonstrate the tangible impact of your problem-solving efforts.

What are Problem Solving Skills? 

Problem-solving is the ability to identify a problem, prioritize based on gravity and urgency, analyze the root cause, gather relevant information, develop and evaluate viable solutions, decide on the most effective and logical solution, and plan and execute implementation. 

Problem-solving encompasses other skills that can be showcased in an interview response and your resume. Problem-solving skills examples include:

• Critical thinking
• Analytical skills
• Decision making
• Research skills
• Technical skills
• Communication skills
• Adaptability and flexibility

Why is Problem Solving Important in the Workplace?

Problem-solving is essential in the workplace because it directly impacts productivity and efficiency. Whenever you encounter a problem, tackling it head-on prevents minor issues from escalating into bigger ones that could disrupt the entire workflow. 

Beyond maintaining smooth operations, your ability to solve problems fosters innovation. It encourages you to think creatively, finding better ways to achieve goals, which keeps the business competitive and pushes the boundaries of what you can achieve. 

Effective problem-solving also contributes to a healthier work environment; it reduces stress by providing clear strategies for overcoming obstacles and builds confidence within teams. 

Examples of Problem-Solving in the Workplace

• Correcting a mistake at work, whether it was made by you or someone else
• Overcoming a delay at work through problem solving and communication
• Resolving an issue with a difficult or upset customer
• Overcoming issues related to a limited budget, and still delivering good work through the use of creative problem solving
• Overcoming a scheduling/staffing shortage in the department to still deliver excellent work
• Troubleshooting and resolving technical issues
• Handling and resolving a conflict with a coworker
• Solving any problems related to money, customer billing, accounting and bookkeeping, etc.
• Taking initiative when another team member overlooked or missed something important
• Taking initiative to meet with your superior to discuss a problem before it became potentially worse
• Solving a safety issue at work or reporting the issue to those who could solve it
• Using problem solving abilities to reduce/eliminate a company expense
• Finding a way to make the company more profitable through new service or product offerings, new pricing ideas, promotion and sale ideas, etc.
• Changing how a process, team, or task is organized to make it more efficient
• Using creative thinking to come up with a solution that the company hasn’t used before
• Performing research to collect data and information to find a new solution to a problem
• Boosting a company or team’s performance by improving some aspect of communication among employees
• Finding a new piece of data that can guide a company’s decisions or strategy better in a certain area

Problem-Solving Examples for Recent Grads/Entry-Level Job Seekers

• Coordinating work between team members in a class project
• Reassigning a missing team member’s work to other group members in a class project
• Adjusting your workflow on a project to accommodate a tight deadline
• Speaking to your professor to get help when you were struggling or unsure about a project
• Asking classmates, peers, or professors for help in an area of struggle
• Talking to your academic advisor to brainstorm solutions to a problem you were facing
• Researching solutions to an academic problem online, via Google or other methods
• Using problem solving and creative thinking to obtain an internship or other work opportunity during school after struggling at first

How To Answer “Tell Us About a Problem You Solved”

When you answer interview questions about problem-solving scenarios, or if you decide to demonstrate your problem-solving skills in a cover letter (which is a good idea any time the job description mentions problem-solving as a necessary skill), I recommend using the STAR method.

STAR stands for:

It’s a simple way of walking the listener or reader through the story in a way that will make sense to them. 

Start by briefly describing the general situation and the task at hand. After this, describe the course of action you chose and why. Ideally, show that you evaluated all the information you could given the time you had, and made a decision based on logic and fact. Finally, describe the positive result you achieved.

Note: Our sample answers below are structured following the STAR formula. Be sure to check them out!

EXPERT ADVICE

Dr. Kyle Elliott , MPA, CHES Tech & Interview Career Coach caffeinatedkyle.com

How can I communicate complex problem-solving experiences clearly and succinctly?

Before answering any interview question, it’s important to understand why the interviewer is asking the question in the first place.

When it comes to questions about your complex problem-solving experiences, for example, the interviewer likely wants to know about your leadership acumen, collaboration abilities, and communication skills, not the problem itself.

Therefore, your answer should be focused on highlighting how you excelled in each of these areas, not diving into the weeds of the problem itself, which is a common mistake less-experienced interviewees often make.

Tailoring Your Answer Based on the Skills Mentioned in the Job Description

As a recruiter, one of the top tips I can give you when responding to the prompt “Tell us about a problem you solved,” is to tailor your answer to the specific skills and qualifications outlined in the job description. 

Once you’ve pinpointed the skills and key competencies the employer is seeking, craft your response to highlight experiences where you successfully utilized or developed those particular abilities. 

For instance, if the job requires strong leadership skills, focus on a problem-solving scenario where you took charge and effectively guided a team toward resolution. 

By aligning your answer with the desired skills outlined in the job description, you demonstrate your suitability for the role and show the employer that you understand their needs.

Amanda Augustine expands on this by saying:

“Showcase the specific skills you used to solve the problem. Did it require critical thinking, analytical abilities, or strong collaboration? Highlight the relevant skills the employer is seeking.”  

Interview Answers to “Tell Me About a Time You Solved a Problem”

Now, let’s look at some sample interview answers to, “Give me an example of a time you used logic to solve a problem,” or “Tell me about a time you solved a problem,” since you’re likely to hear different versions of this interview question in all sorts of industries.

The example interview responses are structured using the STAR method and are categorized into the top 5 key problem-solving skills recruiters look for in a candidate.

1. Analytical Thinking

Situation: In my previous role as a data analyst , our team encountered a significant drop in website traffic.

Task: I was tasked with identifying the root cause of the decrease.

Action: I conducted a thorough analysis of website metrics, including traffic sources, user demographics, and page performance. Through my analysis, I discovered a technical issue with our website’s loading speed, causing users to bounce. 

Result: By optimizing server response time, compressing images, and minimizing redirects, we saw a 20% increase in traffic within two weeks.

2. Critical Thinking

Situation: During a project deadline crunch, our team encountered a major technical issue that threatened to derail our progress.

Task: My task was to assess the situation and devise a solution quickly.

Action: I immediately convened a meeting with the team to brainstorm potential solutions. Instead of panicking, I encouraged everyone to think outside the box and consider unconventional approaches. We analyzed the problem from different angles and weighed the pros and cons of each solution.

Result: By devising a workaround solution, we were able to meet the project deadline, avoiding potential delays that could have cost the company $100,000 in penalties for missing contractual obligations.

3. Decision Making

Situation: As a project manager , I was faced with a dilemma when two key team members had conflicting opinions on the project direction.

Task: My task was to make a decisive choice that would align with the project goals and maintain team cohesion.

Action: I scheduled a meeting with both team members to understand their perspectives in detail. I listened actively, asked probing questions, and encouraged open dialogue. After carefully weighing the pros and cons of each approach, I made a decision that incorporated elements from both viewpoints.

Result: The decision I made not only resolved the immediate conflict but also led to a stronger sense of collaboration within the team. By valuing input from all team members and making a well-informed decision, we were able to achieve our project objectives efficiently.

4. Communication (Teamwork)

Situation: During a cross-functional project, miscommunication between departments was causing delays and misunderstandings.

Task: My task was to improve communication channels and foster better teamwork among team members.

Action: I initiated regular cross-departmental meetings to ensure that everyone was on the same page regarding project goals and timelines. I also implemented a centralized communication platform where team members could share updates, ask questions, and collaborate more effectively.

Result: Streamlining workflows and improving communication channels led to a 30% reduction in project completion time, saving the company $25,000 in operational costs.

5. Persistence 

Situation: During a challenging sales quarter, I encountered numerous rejections and setbacks while trying to close a major client deal.

Task: My task was to persistently pursue the client and overcome obstacles to secure the deal.

Action: I maintained regular communication with the client, addressing their concerns and demonstrating the value proposition of our product. Despite facing multiple rejections, I remained persistent and resilient, adjusting my approach based on feedback and market dynamics.

Result: After months of perseverance, I successfully closed the deal with the client. By closing the major client deal, I exceeded quarterly sales targets by 25%, resulting in a revenue increase of $250,000 for the company.

Tips to Improve Your Problem-Solving Skills

Throughout your career, being able to showcase and effectively communicate your problem-solving skills gives you more leverage in achieving better jobs and earning more money .

So to improve your problem-solving skills, I recommend always analyzing a problem and situation before acting.

 When discussing problem-solving with employers, you never want to sound like you rush or make impulsive decisions. They want to see fact-based or data-based decisions when you solve problems.

Don’t just say you’re good at solving problems. Show it with specifics. How much did you boost efficiency? Did you save the company money? Adding numbers can really make your achievements stand out.

To get better at solving problems, analyze the outcomes of past solutions you came up with. You can recognize what works and what doesn’t.

Think about how you can improve researching and analyzing a situation, how you can get better at communicating, and deciding on the right people in the organization to talk to and “pull in” to help you if needed, etc.

Finally, practice staying calm even in stressful situations. Take a few minutes to walk outside if needed. Step away from your phone and computer to clear your head. A work problem is rarely so urgent that you cannot take five minutes to think (with the possible exception of safety problems), and you’ll get better outcomes if you solve problems by acting logically instead of rushing to react in a panic.

You can use all of the ideas above to describe your problem-solving skills when asked interview questions about the topic. If you say that you do the things above, employers will be impressed when they assess your problem-solving ability.

More Interview Resources

• 3 Answers to “How Do You Handle Stress?”
• How to Answer “How Do You Handle Conflict?” (Interview Question)
• Sample Answers to “Tell Me About a Time You Failed”

About the Author

Biron Clark is a former executive recruiter who has worked individually with hundreds of job seekers, reviewed thousands of resumes and LinkedIn profiles, and recruited for top venture-backed startups and Fortune 500 companies. He has been advising job seekers since 2012 to think differently in their job search and land high-paying, competitive positions. Follow on Twitter and LinkedIn .

Read more articles by Biron Clark

About the Contributor

Kyle Elliott , career coach and mental health advocate, transforms his side hustle into a notable practice, aiding Silicon Valley professionals in maximizing potential. Follow Kyle on LinkedIn .

About the Editor

Hayley Jukes is the Editor-in-Chief at CareerSidekick with five years of experience creating engaging articles, books, and transcripts for diverse platforms and audiences.

Continue Reading

12 Expert-Approved Responses to ‘What Makes You Unique?’ in Job Interviews

15 most common pharmacist interview questions and answers, 15 most common paralegal interview questions and answers, top 30+ funny interview questions and answers, 60 hardest interview questions and answers, 100+ best ice breaker questions to ask candidates, top 20 situational interview questions (& sample answers), 15 most common physical therapist interview questions and answers.

• Home   |  
• About   |  
• Contact Us   |  
• Privacy   |  
• Newsletter   |  
• Shop   |  
• 🔍 Search Site
• Easter Color By Number Sheets
• Printable Easter Dot to Dot
• Easter Worksheets for kids
• Kindergarten
• All Generated Sheets
• Place Value Generated Sheets
• Addition Generated Sheets
• Subtraction Generated Sheets
• Multiplication Generated Sheets
• Division Generated Sheets
• Money Generated Sheets
• Negative Numbers Generated Sheets
• Fraction Generated Sheets
• Place Value Zones
• Number Bonds
• Addition & Subtraction
• Times Tables
• Fraction & Percent Zones
• All Calculators
• Fraction Calculators
• Percent calculators
• Area & Volume Calculators
• Age Calculator
• Height Calculator
• Roman Numeral Calculator
• Coloring Pages
• Fun Math Sheets
• Math Puzzles
• Mental Math Sheets
• Online Times Tables
• Online Addition & Subtraction
• Math Grab Packs
• All Math Quizzes
• Kindergarten Math Quizzes
• 1st Grade Quizzes
• 2nd Grade Quizzes
• 3rd Grade Quizzes
• 4th Grade Quizzes
• 5th Grade Quizzes
• 6th Grade Math Quizzes
• Place Value
• Rounding Numbers
• Comparing Numbers
• Number Lines
• Prime Numbers
• Negative Numbers
• Roman Numerals
• Subtraction
• Add & Subtract
• Multiplication
• Fraction Worksheets
• Learning Fractions
• Fraction Printables
• Percent Worksheets & Help
• All Geometry
• 2d Shapes Worksheets
• 3d Shapes Worksheets
• Shape Properties
• Geometry Cheat Sheets
• Printable Shapes
• Coordinates
• Measurement
• Math Conversion
• Statistics Worksheets
• Bar Graph Worksheets
• Venn Diagrams
• All Word Problems
• Finding all possibilities
• Logic Problems
• Ratio Word Problems
• All UK Maths Sheets
• Year 1 Maths Worksheets
• Year 2 Maths Worksheets
• Year 3 Maths Worksheets
• Year 4 Maths Worksheets
• Year 5 Maths Worksheets
• Year 6 Maths Worksheets
• All AU Maths Sheets
• Kindergarten Maths Australia
• Year 1 Maths Australia
• Year 2 Maths Australia
• Year 3 Maths Australia
• Year 4 Maths Australia
• Year 5 Maths Australia
• Meet the Sallies
• Certificates

Math Logic Problems

Welcome to our Math Logic Problems worksheets. All the problems on this page require children to use their reasoning and logic thinking skills to solve.

There are a range of worksheets on this page with varying levels of difficulty from 1st grade up to 5th grade.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

Logic puzzle problems are a set of problems which involve children using their reasoning and logical thinking skills.

Sometimes children who struggle in other areas of math, such as number work, find that this is an area which they excel in.

Some of the math logic problems on this page work like traditional logic puzzles with table grids to fill in, but most of the sheets simply involve children using their thinking and resoning to solve the problems on the page.

All the logic puzzle worksheets on this page come with an answer sheet.

The problems on this page all involving solving Logic Problems.

Some of the sheets on this page include tables and way to support children with their recording and organising their work.

Some of the sheets have a space for children to record their own thinking and working out, with no support in recording.

The level of the worksheets goes from 1st grade to 5th grade (UK Years 1 to 6).

Using these sheets will help your child to:

• deveolop their reasoning and thinking skills;
• support and develop recording skills;
• solve a range of logic puzzles.

Logic Problems Worksheets

1st grade problems, share the treasure.

Share the Treasure involves sharing out 20 gold bars equally into 4 piles. The second part of the activity involves sharing out the bars using four rules.

• Share the Treasure 1
• PDF version
• Who Chose Which Shape #1

Who Chose Which Shape is a logic problem where children have to work out which salamander chose which shape from the clues given.

2nd Grade Problems

• Birthday Girl

Birthday Girl is an activity which involves finding the correct ages of all the people in the challeges using the clues that are given.

• Share the Treasure #2

Share the Treasure is a logic acitivity where the aim is to share some treasure according to certain criteria.

• Who Chose Which Shape #2

Who Chose Which Shape is a math logic problem where children have to work out which salamander chose which shape from the clues given.

3rd Grade Problems

• Color that Shape

Color that Shape is a coloring activity which uses logical thinking to work out which shape needs to be shaded which color.

Join Me Up is an logical puzzle where the aim is to place the numbers from 1 to 7 into the puzzle so that no consecutive numbers are next to each other.

• Spot the Digits

Spot the Digits is a logic activity where children have to find out the values of the letters a, b, c and d. The values can be determined by using the 3 clues.

4th Grade Problems

Quadra's magic bag challenges.

Quadra's Magic Bag Challenges involves using thinking and reasoning skills to work out two math challenges. The challenges also involve an element of trial and improvement, and also some addition.

• Quadra's Magic Bag Challenge
• Four Dogs Problem

Four Dogs Problem is a logic problem which involves using the clues to work out the owners for each of the four dogs.

Who Caught the Biggest FIsh?

Who Caught the Biggest Fish is a logical number problem where you need to use trial and improvement strategies to work out the order of size of the fish from the clues given about their weights.

• Who Caught the Biggest Fish?

5th Grade Problems

• Who Chose Which?

Who Chose Which is a logical number activity where you need to use the clues to work out which numbers each of the salamanders chose.

• Birthday Bonanza

Birthday Bonanza is a logic problem which requires logical thinking to work out who got which present and how old each of them was.

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

Other Word Problems by the Math Salamanders

Finding all possibilities problems.

This is our finding all possibilities area where all the worksheets involve finding many different answers to the problem posed.

The sheets here encourage systematic working and logical thinking.

The problems are different in that, there is typically only one problem per sheet, but the problem may take quite a while to solve!

• Finding all Possibilities problems

Math Real-Life Word Problems by Grade

We have a variety of different problem solving worksheets, including 'real-life' problems.

The sheets go from 1st through 5th grade.

• Math Problems for Children 1st Grade
• 2nd Grade Math Word Problems
• Math Word Problems for kids 3rd Grade
• 4th Grade Math Word Problems
• 5th Grade Math Problems

Fraction Problems

Here you will find a range of fraction word problems to help your child apply their fraction learning.

The worksheets cover a range of fraction objectives, from adding and subtracting fractions to working out fractions of numbers. The sheets support fraction learning from 2nd grade to 5th grade.

• Fraction Riddles for kids (easier)
• Free Printable Fraction Riddles (harder)

Ratio Problems

Here you will find a range of ratio word problems to help your child understand what a ratio is and how ratios work.

The sheets support ratio learning at a 5th grade level.

We hope you have enjoyed our Math Logic Problems on this page. Please leave a comment at the bottom of the page if you like them!

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

Subscribe to Math Salamanders News

Sign up for our newsletter to get free math support delivered to your inbox each month. Plus, get a seasonal math grab pack included for free!

• Newsletter Signup

Return to Math Problem Worksheets

Return from Finding All Possibilities page to Math Salamanders Homepage

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

New! Comments

TOP OF PAGE

© 2010-2024 Math Salamanders Limited. All Rights Reserved.

• Privacy Policy
• Copyright Policy

• Accounting & Finance
• Communication
• Critical Thinking
• Marketing & Strategy
• Starting a Business
• Team Management
• Corporate Philosophy
• Diversity, Equity, & Inclusion
• Kokorozashi
• Sustainable Business
• AI Ventures
• Machine Learning
• Alumni Voices
• Yoshito Hori Blog
• Unlimited Insights
• Career Skills

The Logic Tree: The Ultimate Critical Thinking Framework

Critical Thinking: Problem-Solving

Problem-solving is a central business skill, and yet it's the one many people struggle with most. This course will show you how to apply critical thinking techniques to common business examples, avoid misunderstandings, and get at the root of any problem.

Logical thinking is the most valuable asset any business professional can have. That's why logic trees are such a valuable tool—they can help you identify a problem, break it down, and build it back up to a solution.

MECE Principle

Using the MECE principle can help ensure you categorize without gaps or overlaps. Check out this course from GLOBIS Unlimited for a practical demonstration of how it works!

If you work in business—any aspect of a business, from R&D to sales to back-office data entry—you’ve probably experienced an unpleasant surprise or two. Not every marketing campaign boosts sales the way we want. Not every event has the turnout we hope for. Not every promotion we expect comes our way.

Particularly with problems that have fiscal casualties, you’ll want to do a little analysis and find out what happened. And one of the absolute best tools to apply to your analysis is critical thinking.

Critical thinking applies logic to solve problems systematically. According to the World Economic Forum’s “Future of Jobs Report” in 2020, “The top skills . . . which employers see as rising in prominence in the lead up to 2025 include . . . critical thinking and analysis, as well as problem-solving.”

And 2020 wasn’t the first year critical thinking made the list.

When it comes to problem-solving, logic trees are a go-to critical thinking framework. Done right, they’ll get you to the root of a problem (pun intended) and even help you find solutions.

What is a logic tree?

A logic tree takes a complex problem and breaks it up systematically, drilling down into smaller, more manageable components. If you’ve seen an image like this, you’ve seen a logic tree:

Looks pretty simple, right? It is! But there are some important rules to follow to make sure your logic tree grows up big and strong—and, more importantly, leads you to the answers you seek.

The Logic Tree and the Case of the Missing Sandwich

Logic trees are often used for complex issues, which is why they’re also called “issue trees” or “decision trees.” But consider a simple (though still frustrating) problem faced by many office workers in the days before COVID-19 . . .

It’s lunchtime at your workplace, so you head to the office fridge—only to find your lunch is gone. You stare in disbelief at the empty space where your sandwich should be. A mocking smudge of condensation stares back.

As you are a logical person (not prone to throwing tantrums), you decide to approach this problem with critical thinking . You march back to your desk, grab a pen and paper, and write down four words: “Who took my sandwich?”

You’ve planted your logic tree.

Decide what you really need to know.

Before you jump into the branches, remind yourself that logic trees stem from problems—but knee-jerk responses often misidentify problems. So once you’ve got your initial question down, take a step back. Is there a branch that should have come before the first one you made?

Setting aside the sandwich problem for just a moment, consider you’re exploring a different issue: “How can I get promoted?” Think about the reason you’re asking that question. What’s the actual problem you need to solve?

Maybe you should have asked, “How can I earn more money?” That opens far more possibilities than just getting promoted—you could look for another job, start a side business, or invest in your buddy’s startup. “How can I get promoted?” becomes just one branch on a bigger tree.

This is how logic trees (and critical thinking in general) not only help you identify solutions, but think outside the box —innovate.

Beware emotional bias in the branches.

You decide to start your logic tree with “Who took my sandwich?” From that root problem, you might break up the question into its seemingly logical components: “someone inside the office ate my sandwich” (Mary Anne, maybe? Or Phil?) and “someone came in off the street and stole it” (a hungry ninja, perhaps?).

Already, your logic tree is telling you something important.

The fact that you’ve defined the first two branches of your logic tree as “culprit here or there” means you’re sure there’s a thief in your midst. You’ve (perhaps subconsciously) ruled out the possibility that you forgot your sandwich at home or left it on the bus. The logic tree you’ve started will also not remind you if you didn’t make a lunch at all today because you’ll be eating out with Mary Anne and Phil.

Logic trees will only tell you what you ask them to tell you. They can only answer the questions you lay down. Don’t let your emotions limit the possibilities. Try to be aware of the assumptions you’re baking in.

Next Article

3 Ways the MECE Principle Makes Data Organization Easy

Apply MECE to the branches of your logic tree.

Now that you’ve got your first two branches, you set to work breaking them down further. This is a good time to remember to follow the MECE principle . MECE stands for “mutually exclusive, collectively exhaustive.” In other words, it means you want to build the branches of your logic tree without gaps or duplicates.

Remember, logic trees are a critical thinking tool, and critical thinking is about systematic problem-solving. The MECE component of logic trees helps keep the system clean by eliminating possibilities, which increases efficiency toward finding an answer.

For example, if one branch says, “Someone in the office took my sandwich” and another says, “Someone on this floor took my sandwich,” you’re setting yourself up for some overlap. (Surely, this floor is in the office, no?)

It seems unlikely that someone came in off the street and took your sandwich, so you focus on the other possibility: an inside job. That leads to two new MECE-friendly branches: someone from your team, or someone from another team? Then more branches under those: Someone who decided your lunch looked way more delicious than their own, or someone who innocently mistook your lunch for theirs?

Aha! Looking at the breakdown, the answer strikes you. You bought that sandwich from Sandwich Heaven—the same place your teammate Rick sometimes buys his lunch. You check the fridge again, and sure enough, there’s another sandwich almost identical to yours (except this one has tomato, gross).

Don’t expect logic trees to end with “the answer.”

Logic trees aren’t about quick fixes. They’re about training your mind to reach reliable solutions.

While you may be tempted to rush off and have a chat with Rick about stealing your sandwich, it’ll serve you much better to reflect on why he took your sandwich in the first place. You and Rick bought sandwiches from the same shop, which makes it easy to mix them up. That may be the answer—but is it a solution ?

At the end of your logic tree, pose some further questions: Should you and Rick decide to put your sandwiches on different shelves in the fridge? Should you make it a point to label yours with your name? Or should you stop going to Sandwich Heaven every day?

This follow-up is important, even for logic trees targeting more serious issues. If you’re trying to determine why sales are down, perhaps your logic tree will reveal you’re targeting the wrong customers. In that case, what steps can you take to reset your targets?

The Payoff of Learning Logic Trees

While they might sound like a lot of work (and yes, they can be a bit overwhelming at first), logic trees can actually save you a lot of time once you get the hang of them. Even better, you don’t have to slave away at mastering them on your own. There’s no reason a logic tree needs to be a solitary activity (even if you’re hunting down a sandwich thief).

In fact, if you’re working on a critical business issue, you really shouldn’t try to go it alone. Ask your boss, your team, a consultant, or another colleague to review your work. They don’t even have to understand the problem in depth—the point is to get a fresh pair of eyes on your logic tree and, by extension, your problem.

Finally, keep in mind that there’s no guarantee a logic tree will bring you to the perfect answer. What they will do is train your critical thinking skills and help widen your view of the problems you face.

Related Articles

Uniquely feminine traits of successful female leaders.

The Foreign Entrepreneur’s Guide to Securing a Japan Investor Visa

The Trap of Tiara Syndrome: How to Advocate for Yourself

Get monthly Insights

Sign up for our newsletter! Privacy Policy

GLOBIS Insights

• Submission Guidelines
• Our Contributors

Accountability

• Privacy Policy

GLOBIS Group

• GLOBIS Corporation
• GLOBIS University
• GLOBIS Capital Partners
• GLOBIS Asia Pacific
• GLOBIS Asia Campus
• GLOBIS China
• GLOBIS Europe
• GLOBIS Thailand
• G1 Institute
• Ibaraki Robots Sports Entertainment
• KIBOW Foundation

© GLOBIS All Rights Reserved

Explore Jobs

• Jobs Near Me
• Remote Jobs
• Full Time Jobs
• Part Time Jobs
• Entry Level Jobs
• Work From Home Jobs

Find Specific Jobs

• $15 Per Hour Jobs
• $20 Per Hour Jobs
• Hiring Immediately Jobs
• High School Jobs
• H1b Visa Jobs

Explore Careers

• Business And Financial
• Architecture And Engineering
• Computer And Mathematical

Explore Professions

• What They Do
• Certifications
• Demographics

Best Companies

• Health Care
• Fortune 500

Explore Companies

• CEO And Executies
• Resume Builder
• Career Advice
• Explore Majors
• Questions And Answers
• Interview Questions

The Most Important Logical Thinking Skills (With Examples)

• Logical Skills
• Promotional Skills
• Bookkeeping Skills
• Typing Skills
• Sales Skills
• Science And Math Skills
• Physical Strength And Dexterity Skills
• Customer Service Skills
• Instructional Skills
• Logical-Thinking Skills
• Mechanical Skills
• Memorization Skills
• Motivational Skills
• Artistic Talent

Find a Job You Really Want In

Logical thinking skills like critical-thinking, research, and creative thinking are valuable assets in the workplace. These skills are sought after by many employers, who want employees that take into account facts and data before deciding on an important course of action. This is because such solutions will ensure the organization’s processes can continue to operate efficiently. So, if you’re a job seeker or employee looking to explore and brush up on your logical thinking skills, you’re in luck. This article will cover examples of logical thinking skills in the workplace, as well as what you can do to showcase those skills on your resume and in interviews. Key Takeaways: Logical thinking is problem solving based on reasoning that follows a strictly structured progression of analysis. Critical thinking, research, creativity, mathematics, reading, active listening, and organization are all important logical thinking skills in the workplace. Logical thinking provides objectivity for decision making that multiple people can accept. Deduction follows valid premises to reach a logical conclusion. It can be very helpful to demonstrate logical thinking skills at a job interview. In This Article    Skip to section What is logical thinking? 10 examples of logical thinking skills Examples of logical thinking in the workplace What is deductive reasoning? Logical thinking in a job interview Logical thinking skills FAQ Final thoughts References Sign Up For More Advice and Jobs Show More What is logical thinking?

Logical thinking is the ability to reason out an issue after observing and analyzing it from all angles . You can then form a conclusion that makes the most sense. It also includes the ability to take note of reactions and feedback to aid in the formation of the conclusion.

Logical thinking skills enable you to present your justification for the actions you take, the strategies you use, and the decisions you make. You can easily stand in front of your clients, peers, and supervisors and defend your product, service, and course of action if the necessity arises.

Logical thinking is an excellent way of solving complex problems. You can break the problem into smaller parts; solve them individually in a sequence, then present the complete solution. However, it is not infallible.

So, when a problem in the workplace feels overwhelming, you may want to think about it logically first.

10 examples of logical thinking skills

Logical thinking skills are a skill set that enables you to reason logically when solving problems. They enable you to provide well-reasoned answers to any issues that arise. They also empower you to make decisions that most people will consider rational.

Critical-thinking skills. If you are a critical thinker, then you can analyze and evaluate a problem before making judgments. You need to improve your critical thinking process to become a logical thinker.

Your critical thinking skills will improve your ability to solve problems. You will be the go-to employee concerning crises. People can rely on you to be reasonable whenever an issue arises instead of letting biases rule you.

Research skills. If you are a good researcher , then you can search and locate data that can be useful when presenting information on your preferred subject.

The more relevant information you have about a particular subject, the more accurate your conclusions are likely to be. The sources you use must be reputable and relevant.

For this reason, your ability to ferret out information will affect how well you can reason logically.

Creative thinking skills. If you are a creative thinker , then you can find innovative solutions to problems.

You are the kind of person that can think outside the box when brainstorming ideas and potential solutions. Your thinking is not rigid. Instead, you tend to look at issues in ways other people have not thought of before.

While logical thinking is based on data and facts, that doesn’t mean it is rigid. You can creatively find ways of sourcing that data or experimenting so that you can form logical conclusions. Your strategic thinking skills will also help enable you to analyze reactions or collect feedback .

Mathematical skills. If you are skilled in mathematics , then you can work well with numbers and represent mathematical ideas using visual symbols. Your brain must be able to compute information.

Business is a numbers game. That means you must have some knowledge of mathematics. You must be able to perform basic mathematical tasks involving addition, subtractions, divisions, multiplications, etc.

So, to become a logical thinker, you must be comfortable working with numbers. You will encounter them in many business-related complex problems. And your ability to understand them will determine whether you can reach an accurate logical conclusion that helps your organization.

Reading skills. If you are a good reader , then you can make sense of the letters and symbols that you see. Your ability to read will determine your competency concerning your logical thinking and reasoning skills.

And that skill set will come in handy when you are presented with different sets of work-related statements from which you are meant to conclude. Such statements may be part of your company policy, technical manual, etc.

Active listening skills. Active listening is an important communication skill to have. If you are an active listener, then you can hear, understand what is being said, remember it, and respond to it if necessary.

Not all instructions are written. You may need to listen to someone to get the information you need to solve problems before you write it down. In that case, your active listening skills will determine how well you can remember the information so that you can use it to reason things out logically.

Information ordering skills. If you have information ordering skills, then you can arrange things based on a specified order following the set rules or conditions. These things may include mathematical operations, words, pictures, etc.

Different organizations have different business processes. The workflow in one organization will be not similar to that of another organization even if both belong to the same industry.

Your ability to order information will depend on an organization’s culture . And it will have a major impact on how you can think and reason concerning solutions to your company problems.

If you follow the wrong order, then no matter how good your problem-solving techniques are your conclusions may be wrong for your organization.

Persuasion skills. Logical thinking can be useful when persuading others, especially in the workplace.

For example, lets say one of your co-workers wants to take a project in an impulsive direction, which will increase the budget. However, after you do your research, you realize a budget increase would be impossible.

You can then use your logical thinking skills to explain the situation to your co-worker , including details facts and numbers, which will help dissuade them from making an uninformed decision.

Decision making skills. Decision making skills go hand and hand with logical thinking, as being able to think logically about solutions and research topics will make it far easier to make informed decisions.

After all, no one likes making a decision that feels like a shot in the dark, so knowing crucial information about the options aviable to you, and thinking about them logically, can improve your confidence around decision making.

Confidence skills. Confidence that stems from an emotional and irrational place will always be fragile, but when you have more knowledge available to you through logical thinking, you can be more confident in your confidence skills.

For instance, if an employee asked you to answer an important question, you will have a lot more confidence in your answer if you can think logically about it, as opposed to having an air of uncertainty.

Examples of logical thinking in the workplace

To improve your logic skills, it would be wise to practice how to solve problems based on facts and data. Below are examples of logical thinking in the workplace that will help you understand this kind of reasoning so that you can improve your thinking:

The human resource department in your organization has determined that leadership skills are important for anyone looking to go into a senior management position. So, it decides that it needs proof of leadership before hiring anyone internally. To find the right person for the senior management position , every candidate must undertake a project that involves a team of five. Whoever leads the winning team will get the senior managerial position.

This example shows a logical conclusion that is reached by your organization’s human resource department. In this case, your HR department has utilized logical thinking to determine the best internal candidate for the senior manager position.

It could be summarized as follows:

Statement 1: People with excellent leadership skills that produce winning teams make great senior managers. Statement 2: Candidate A is an excellent leader that has produced a winning team. Conclusion: Candidate A will make an excellent senior manager .

A marketing company researches working women on behalf of one of their clients – a robotics company. They find out that these women feel overwhelmed with responsibilities at home and in the workplace. As a result, they do not have enough time to clean, take care of their children, and stay productive in the workplace. A robotics company uses this research to create a robot cleaner that can be operated remotely . Then they advertise this cleaner specifically to working women with the tag line, “Working women can do it all with a little bit of help.” As a result of this marketing campaign, their revenues double within a year.

This example shows a logical conclusion reached by a robotics company after receiving the results of marketing research on working women. In this case, logical thinking has enabled the company to come up with a new marketing strategy for their cleaning product.

Statement 1: Working women struggle to keep their homes clean. Statement 2: Robot cleaners can take over cleaning duties for women who struggle to keep their homes clean. Conclusion: Robot cleaner can help working women keep their homes clean.

CalcX. Inc. has created a customer survey concerning its new finance software. The goal of the survey is to determine what customers like best about the software. After reading through over 100 customer reviews and ratings, it emerges that 60% of customers love the new user interface because it’s easy to navigate. CalcX. Inc. then decides to improve its marketing strategy. It decides to train every salesperson to talk about the easy navigation feature and how superior it is to the competition. So, every time a client objects to the price, the sales rep could admit that it is expensive, but the excellent user interface makes up for the price. At the end of the year, it emerges that this strategy has improved sales revenues by 10%.

The above example shows how logical thinking has helped CalcX. Sell more software and improve its bottom line.

Statement 1: If the majority of customers like a particular software feature, then sales reps should use it to overcome objections and increase revenues. Statement 2: 60% of the surveyed customers like the user interface of the new software, and; they think it makes navigation easier. Conclusion: The sales reps should market the new software’s user interface and the fact that it is easy to navigate to improve the company’s bottom line.

A political candidate hires a focus group to discuss hot-button issues they feel strongly about. It emerges that the group is torn on sexual reproductive health issues, but most support the issue of internal security . However, nearly everyone is opposed to the lower wages being paid due to the current economic crisis. Based on the results of this research, the candidate decides to focus on improving the economy and security mechanisms in the country. He also decides to let go of the sexual productive health issues because it would potentially cause him to lose some support.

In this case, the political candidate has made logical conclusions on what topics he should use to campaign for his seat with minimal controversies so that he doesn’t lose many votes.

This situation could be summarized as follows:

Statement 1: Most people find sexual reproductive health issues controversial and cannot agree. Statement 2: Most people feel that the internal security of the country is in jeopardy and something should be done about it. Statement 3: Most people want higher wages and an improved economy. Statement 4: Political candidates who want to win must avoid controversy and speak up on things that matter to people. Conclusion: To win, political candidates must focus on higher wages, an improved economy, and the internal security of the country while avoiding sexual reproductive health matters.

What is deductive reasoning?

Deductive reasoning is an aspect of logical reasoning. It is a top-down reasoning approach that enables you to form a specific logical conclusion based on generalities. Therefore, you can use one or more statements, usually referred to as premises, to conclude something.

For example:

Statement 1: All mothers are women Statement 2: Daisy is a mother. Conclusion: Daisy is a woman.

Based on the above examples, all mothers are classified as women, and since Daisy is a mother, then it’s logical to deduce that she is a woman too.

It’s worth noting though, that deductive reasoning does not always produce an accurate conclusion based on reality.

Statement 1: All caregivers in this room are nurses. Statement 2: This dog, Tom, is a caregiver . Conclusion: This dog, Tom, is a nurse .

From the above example, we have deduced that Tom, the dog, is a nurse simply because the first statement stated that all caregivers are nurses. And yet, in reality, we know that dogs cannot be nurses. They do not have the mental capacity to become engaged in the profession.

For this reason, you must bear in mind that an argument can be validly based on the conditions but it can also be unsound if some statements are based on a fallacy.

Logical thinking in a job interview

Since logical thinking is so important in the workplace, most job interviewers will want to see you demonstrate this skill at the job interview. It is very important to keep in mind your logical thinking skills when you talk about yourself at the interview.

There are many ways in which an interviewer may ask you to demonstrate your logical thinking skills. For example:

You may have to solve an example problem. If the interviewer provides you a problem similar to one you might find at your job, make sure to critically analyze the problem to deduce a solution.

You may be asked about a previous problem or conflict you had to solve. This classic question provides you the opportunity to show your skills in action, so make sure to highlight the objectivity and logic of your problem solving.

Show your logic when talking about yourself. When given the opportunity to talk about yourself, highlight how logic comes into play in your decision making. This could be in how you picked the job position, why you choose your career or education, or what it is about yourself that makes you a great candidate.

Logical thinking skills FAQ

Why is it important to think logically?

It’s important to think logically because it allows you to analyze a situation and come up with a logical solution. It allows for you to reason through the important decisions and solve problems with a better understanding of what needs to be done. This is necessary for developing a strong career.

Why is logic important?

Logic is important because it helps develop critical thinking skills. Critical thinking skills are important because they help you analyze and evaluate a problem before you make a decision. It also helps you improve your problem-solving skills to allow you to make better decisions.

How do you improve your logical thinking skills?

When improving your logical thinking skills make sure you spend time on a creative hobby and practice questioning. Creative hobbies can help reduce stress levels, and lower stress leads to having an easier time focusing on tasks and making logical thinking. Creative hobbies can include things like drawing, painting, and writing.

Another way to improve your logical thinking is to start asking questions about things. Asking questions allows for you to discover new things and learn about new topics you may not have thought about before.

What are logical thinking skills you need to succeed at work?

There are many logical thinking skills you need to succeed in the workplace. Our top four picks include:

Observation

Active Listening

Problem-solving

Final thoughts

Logical thinking skills are valuable skills to have. You need to develop them so that you can become an asset to any organization that hires you. Be sure to include them in your resume and cover letter .

And if you make it to the interview, also ensure that you highlight these skills. You can do all this by highlighting the career accomplishments that required you to use logical thinking in the workplace.

It’s Your Yale – Consider Critical Thinking Skills to Articulate Your Work Quality

How useful was this post?

Click on a star to rate it!

Average rating / 5. Vote count:

No votes so far! Be the first to rate this post.

Roger Raber has been a content writer at Zippia for over a year and has authored several hundred articles. Having retired after 28 years of teaching writing and research at both the high school and college levels, Roger enjoys providing career details that help inform people who are curious about a new job or career. Roger holds a BA in English from Cleveland State University and a MA from Marygrove college.

Related posts

How To Include Spatial Orientation Skills In Your Resume

Skill Sets: What Are They?

The Most Important Customer Service Skills (With Examples)

The Most Important Observation Skills (With Examples)

• Career Advice >
• Resume Skills >
• Defined Skills >
• Logical Thinking Skills

• InterviewPenguin.com – Your best job interview coach since 2011

Give me a specific example of a time when you used good judgment and logic in solving a problem – Sample interview answers

Let’s face the reality of 21str century . Relying on Google and smartphones to answer each our question in an instant , and to lead us to any place of our choice, without a need to think , does not help with our intellectual capacities.

The impact of social media is also apparent, with young people struggling to start a conversation with a stranger , or to survive a day (or even an hour) without looking at the screen of their phone. Implications are clearly visible in the workplace. Most people won’t do anything unless you give them exact directions, and when they face a problem, they will ask Google for an answer…

But not everything can be found on Google, and technology cannot solve all our problems. Maybe it creates more problems than it solves . Hence it makes a perfect sense to ask job candidates about a problem they solved with a help of logic, and not with a help of their boss, or a search engine.

Let’s have a look at 7 sample answers to this question. Do not forget to read also the notes below the answers. They will help you to understand which answer you should choose, and what to focus on while talking about this situation in an interview.

7 sample answers to “Give an example of an occasion when you used logic to solve a problem” interview question

• In my last job of  a purchasing agent I had to decide between two suppliers . One had a better offer in terms of price, but they were new on the market, and I could not find any references from their customers. The second supplier was an established company, operational for more than 10 years. They charged 10% more for the same product, but I could contact some of their business partners and verify the quality of the products, and timely delivery. I decided for a second company, because we were looking for a long time partner , and, considering all the criteria I set for my selection, they were simply a more logical choice.
• Working as an HR manager, I remember leading a very close interview for a job of an office assistant. All three shortlisted applicants met the expectations, and they all showed right attitude to work and motivation. But I had to choose one only, and did not want to decide according to my personal preferences . I decided to conduct one more rounds of interviews, and invited more managers to participate and ask questions. At the end each of them should pick the candidate they liked the most, citing the reasons. This really helped me to solve the problem, since they had a different perspective on the issue, and basically all of them chose one particular candidate.
• This is my first job application , so I do not have much experience with solving problems at work with good judgement and logic. However, I solved a lot of mathematical problems with the help of logic , during my lessons in statistical analysis and time row analysis. I must say that I enjoy thinking and using logic to solve a problem, instead of asking someone for help or looking for the most simple solution on Google. That’s not a way to grow intellectually, and to become the best version of yourself, which is a goal I aspire to.
• I was missing some key data while trying to forecast the trends in sales for Q3 last year. Back then I was working as an analyst for a big retail store, they were operational both offline and online. There was a lot of unpredictability in the market, with the pandemic and everything else happening. But we had to have some forecast , because everything starts from there–the orders of products, the recruitment of temporary staff, and so on. I decided to look at the historical data , and apply the same model for analysis which we applied a year before. I do not know if it was a right choice, because I left the company, and do not have the access to their numbers anymore. But s ometimes the most important thing is to make a decision , even though we miss some important information.
• I’ve been using logic all the time in work. In my opinion, there is no place for guesses in healthcare . I always relied on the proven models of examination and diagnosis of illnesses , and followed the patterns and protocols to the point, adhering to strict principles of validity. Of course it still happened that I made a mistake. But I am sure that working in this way, I minimized the number of mistakes. And that’s probably the most we can hope for…
• I had to decide about a certain production process in work . I had on my table three proposals from the employees who worked with the machine, each of them suggesting something different. I validated their arguments, asked them additional questions , and also made practical tests, on a small scale. Eventually, considering pros and cons of each suggestion and the test results, comparing them with the expectations of the top management , I choose one of the processes and we applied it on a large scale in the company.
• I used logic when decided about my field of study . To be honest, I was interested in a variety of subjects, starting with social work and ending with technology. But I also had some goals outside of work, things I wanted to afford, family I planned to start one day in the future . So I looked at the situation on the employment market, which positions are in demand, what is the average salary offer, and how the economy will likely evolve in the future. Considering all arguments, I eventually decided to study information technology. I think it was  good choice. If I manage to get this job with you, I will definitely consider it a great and logical decision.

* Special Tip: Now you know how to answer this one, but what about dozens other tricky scenario-based questions you may face in your interview? Check up to 10 premium answers to each one in our Interview Success Package:

You do not need previous working experience to have experience with problems

If you apply for your first job, you can talk about some problem you solved at school, or even in your personal life . Just think about it for a moment–we solve some problems our entire life, from the moment we are born till the moment we die.

Your attitude matters for the interviewers, and not the particular situation you narrate. If they see that you actually used your brain when facing a problem and didn’t opt for the most immediate solution, that you considered the arguments and weighted pros and cons, and did not decide intuitively, when they see that you eventually decided on your own and did not wait for someone else to tell you what you should do, they will be happy with your answer .

And it doesn’t matter whether you talk about job, relationship, or a lesson in school.

Use numbers to give your story some credibility

You can definitely make something up for your interview–many job seekers do the same thing. Interviewers do not have many options to verify the authenticity of your story .

However, if you talk about a problem vaguely, and do not mention many details, or if you say contradictory things while describing the situation , they won’t believe you. That would be a huge blow to your chances in an interview…

Think carefully about your answer. Write it down. Include some numbers, dates, details . Such things make it easier for the interviewers to imagine the situation you describe , and it will be also easier for them to believe you …

Ready to answer this one? Check also 7 sample answers to other tricky interview questions :

• Interview Success Package – Up to 10 premium answers to all interview questions. Learn something your competitors won’t know, streamline your preparation, and ace your next interview.
• Have you ever worked on a project that was a failure?
• Tell me about a time when you applied technical skills to solve a problem .
• Recent Posts

© InterviewPenguin.com

Privacy Policy