Analytical | Maths | Logical Puzzles for Interview with Answers

Puzzles have had their own place in our lives for since long. They have formed part of our social get-togethers when we use them to while away the time or as part of the social togetherness. In fact, these puzzles are designed for checking the lateral thinking ability of the candidates.

Let us check out a few of the puzzles of various types that would enhance your level of intuitive thinking capabilities.

What Makes Puzzles so Important?

Well, even the tech companies pose a few puzzles to the candidates during the interviews. These include puzzles of a different nature. The puzzles can consist of riddles, guess, and estimation, and those that test your lateral thinking capabilities.

But, do they really matter? Is there any sort of correlation between puzzle-solving capability and job performance? Well, they may not have any direct impact on the effectiveness of a job, but they can be the right ones to understand how you think or how you look at things. They would also give you an idea of how you can figure out of the box. These can also be the right options to help you relax so that you can be tested for the more critical questions. We at TheInterviewTop shall give you some good examples of such puzzles.

Analytical Puzzles for Interview with Answers – A Few Good Examples

The logical puzzles would be an excellent option that can be expected if you are looking for a job in the statistics and data handling. They may be found in other genres as well. A fresh candidate entering a realm may not have the necessary skills, but these questions can be extremely useful in letting the interviewer test the lateral thinking of the candidates. If the candidates possess enough expertise in solving these puzzles, they can be expected to address the real-life scenarios.

Analytical puzzles for interview with answers

Here are a few good examples –

Q- There are three jars with Apples, Oranges, and Mix of Oranges and Apples, respectively. However, the labels on the jars are mismatched. If you want to label the jars properly, how many fruits should you pick from each of the jars?

A – You would indeed need to churn your brain to understand the question correctly. All three jars are labeled incorrectly. So, let us solve it one by one-

The A+O jar will either contain apples or oranges, but it will not have both of them.

So if you pick a fruit from this jar, and you get an Apple, you will label the jar as apple, as it cannot contain A+O. In that case, the third jar cannot get the label as A+O. Ideally speaking, one fruit from each jar would help you label the jar correctly. The third jar will be labeled A+O.

A little confusing? Give it a thought. You should easily understand.

Q- Two trains are moving towards each other on the same track at 40 km per hour. They are 80 km apart. A bird travels between train A and train B at a speed of 100 kmph. It keeps moving from train A to train B and again B to A till the trains collide. What distance would be covered by the bird by the time the trains collide?

A – You need to use both analytical and mathematical skills to solve this puzzle.

The velocity of approaching by two trains – 40+40 km per hour

Time taken for the collision of the trains – 80km at 80km per hour or One Hour.

The total distance covered by the bird in one hour is 100 km per hour. So, the bird travels 100km by the time the trains collide. If you begin calculating the distance between X and Y, you will summarily be rejected.

Q- A birthday cake needs to split into eight equal parts with just three cuts. How would you be able to achieve it?

A – The solution is simple enough if you take care to consider the case with some sort of analytical thinking. Just slice the cake into four parts by cutting it through cuts perpendicular to each other. You get four cakes. Place these four slices, one above the other symmetrically.  Now give the third cut to halve it exactly. You get eight equal pieces.

Q- There are 20 blue and 13 red balls in a bag. You take out two balls at a time. If both are of the same color, they are replaced with one blue ball. If they are of different colors, they are replaced with a red ball. So, what would be the color of the last ball in the bag?

A – That would appear an extremely difficult question. However, if you apply analytical skills, you will find that the red balls always remain in an odd number. If you remove two red balls, you will replace them with a blue ball. If you remove one red and blue, you will replace it with one red. Ideally, for every two balls removed, you will always add one. Thus the last ball will always be a red one.

Q – You have two jugs of 4 and five liters. You need to pour exactly seven liters of water. How would you do it?

A – This will ideally take three steps. Fill the five liters jug and pour the content into the four-liter jug. The five-liter jug will have one liter of water. Pour it into the bucket. Empty the four-litre jug. Now repeat the step to fill one more liter of water into the bucket. The bucket now has two liters of water. Now use the five liters jug to fill the bucket, making it seven liters.

Q – You have two ropes and a lighter. Each rope takes exactly 60 minutes to burn. However, it may not burn consistently, which means the first half may take 10 minutes, and the other half 50 minute. How will you measure 45 minutes?

A – Burn the first rope at both ends and the other one at one end. When the first rope has burnt completely, 30 minutes have passed. Light the second end of the second rope. This rope will take 15 minutes to burn out (half of 30 minutes).

These were a few good analytical puzzles for an interview with answers which shall help you think out of the box and crack the analytical skills interview round.

Mathematical Puzzles – A Few Good Options you can Give a Thought To

Mathematical puzzles are relatively easy and straightforward. This would be easier for the candidates preparing for the technical positions. Here are a few good examples of mathematical puzzles for an interview that should be quite common.

maths puzzles for interview

Q – Three ants are sitting at the three vertices of an equilateral triangle. Each of them decides on a random direction and walks along the side of the triangle. What is the probability that they will not collide?

A – The possibility of avoiding a collision would be possible only of all the three ants move in the same direction. In all the other cases, at least two of the ants will collide with one another. Each of the ants can decide either in a clockwise or anti-clockwise direction. That means it has a 50 percent or one in two probability. The probability calculations help you arrive at this calculation –

No (of no collision) = No of the three ants moving in a clockwise direction + no of the three ants moving in the anti-clockwise direction

= 0.5 x 0.5 x 0.5 + 0.5 x 0.5 x 0.5

= 0.25

That should be your answer.

Q – You have two-hour glasses, each measuring 4 and 7 minutes. How will you calculate 9 minutes using them?

A – Use both hourglasses at once. When the 4-hour hour-glass finished, you have three hours left on the seven hour-glass. You have now calculated for four hours.

Reverse four hour-glass. When the seven hour-glass has finished, you have completed seven hours, and there is one hour left on the four-hour glass. You have completed 7 hours. Reverse the seven-hour glass. Wait till the four-hour glass is completed. You have calculated eight hours. Reverse the seven-hour glass (of course, it has not emptied), and it will complete in one hour.

That completes nine hours.

Q – There are multiple rabbits and chickens in a cage. There is a total of 72 heads and 200 feet. So, how many rabbits and how many chickens are there in the cage?

A – This will involve a simple mathematical calculation and must be rather simple enough.

Let us assume that r is the number of rabbits, and c is the number of chickens. So, as per the calculations,

R+c = 72

4r + 2c = 200. Of course, this should be obvious. Rabbits have four feet and chickens two.

R+c =72

Or 2r+2c = 144

From above, 2c= 144-2r

Using this in the above equation, 4r+2c = 200

4r +144-2r = 200

2r = 200-144

= 56

R= 28

So there are 28 rabbits and 44 chickens.

Q – A person has some money with him. When he passes through a temple, his money gets doubled. He offers Rs100 at every temple. His pocket is empty when he reaches home. He visits a total of four temples. So, what was the money he initially had?

A – Let us assume the money he initially had is X.

At the first temple, he will have 2x -100

At the second temple, his money gets doubled i.e., 2(2x-100) or 4x -200

After donating Rs. 100. The money left with him is 4x-300.

At the third temple, his money will be 8x -600 and after he donates Rs. 100, he is left with 8x -700.

At the fourth temple, his money would be 16x -1400 and after he offers Rs. 100, he is left with 16x -1500.

After the fourth temple, he is left with no money. That means 16x-1500 = 0

Further calculations let you arrive at the following results

16x -1500 = 0

16x =1500

X= 93.75

So, he had Rs. 93.75initially.

Q – There were a total of 66 handshakes at a party. Everyone at the party shaked hands with every other. So, how many people were there at the party?

A – This question was asked at the Infosys written test. Like most other questions in this compilation, this one too needs a simple mathematical calculation.

Let us assume the party had n number of visitors. So the first person will shake hands with everyone else except himself. So, he shakes hands n-1 times.

The second person does it with everyone else, but since we have already counted the first one, he shakes hands with n-2 persons.

Thus the total number of handshakes will be (n-1)+(n-2)+(n-3)+..0

According to the probability theory,

(n-1)*(n-1+1)/2

= (n-1)*n/2

= 66

This further leads

= n^2 -n = 132

(n-12)(n+11) = 0

N is equal to either 12 or n= -11

Since number of people cannot be -11, the right number is 12.

If you are still confused, you can refer to the theory of permutations and combinations to refresh your knowledge.

Q- How many squares does a chessboard have?

A – When you look at it the first time, you will come to the conclusion that it is a wrong entry here. It is neither a mathematical puzzle nor worthy of being a question to be asked in an interview. The answer is simple – 64, and we know it because we have all played or seen chess being played.

But wait, 64 is a wrong answer! It is just the number of individual squares used for placing the pieces and constitutes the playing area. However, what about the other squares formed by the adjoining squares?

You can combine the squares into bigger ones – like 2 x 2, 3 x 3, and so on.

The calculation moves ahead as follows –

1 x 1 squares arranged in 8 x 8 vertical and horizontal lines = 8 x8 = 64 squares

2 x 2 squares can be arranged in 7 x 7 positions = 49

3 x 3 squares are arranged in 6 x6 positions = 36

For 4x 4 positions, number of squares = 25

For 5 x 5, you get 16 squares

For 6 x 6, the number of squares is 9

Likewise, for 7 x 7 and 8 x 8, you get 4 and 1 squares

The total number of squares is 204.

These were some tricky maths questions that can be asked in an interview for any technical rounds. If you are a finance guy or statistical guy, you are definitely going to be tested on this.

A Few Logical Puzzles – They may be Worthy of Checking

While mathematical and analytical puzzles are designed to provide you a look into the analytical ability of the candidate. The logical puzzles are designed to offer you an insight into the thought process of your candidates. The interviewer actually judges your thinking abilities in terms of out of box thinking.

logical puzzles for interview

A few questions of this genre would be interesting enough and add a fun angle to your interview repertoire.

Q – There are two tribes in a foreign land – a Lie Tribe and a Truth Tribe.

You meet three of these people. When you ask the first person which tribe does he belong to. He answers something in his native language, and you do not understand it. The second person says he said he belongs to the Lie tribe. The third person says the second person is lying.

So, which tribe does the third person belong to?

A – Quite tricky. Isn’t it? Not exactly. You should be able to solve it rather quickly and simply.

Here is how you can deduce the right answer.

Let us assume the first person belongs to the Truth tribe. So, he will say he belongs to the truth tribe. So, obviously, the second person is lying. Now from that logic, the third person is telling the truth.

Now assuming the first person belongs to the Lie tribe, he will again say he belongs to the Truth tribe. In this case, once again, the second person is lying. And the third person is telling the truth.

That would let you conclude that the third person belongs to the Truth Tribe.

A few tricky puzzles can include the ones here in this video –

Q – A farmer has a goat, a wolf, and cabbage with him, and he has to cross the river. The boat is smaller, and he can carry only one thing with him to the other bank. How will he carry all three without harming anyone or anything?

A – You can not leave cabbage and goat on the ban alone. Likewise, you cannot leave the goat and wolf together either. The trick would be as here.

He will take the goat with him to the other bank. He will return and take the cabbage with him to the other bank but will bring back the goat. Now, he will leave the goat and take the wolf with him. He will return and take goat finally thus transferring all the three of his belongings to the other bank.

Q – There are two gates in front of you. One leads to the hell and the other to heaven. Both the gates have guards. One of them always tells the truth, while the other always lies. How will you find the door to heaven? You can ask only one question to each of them.

A – It will need you t apply both analytical and logical skills to solve that problem.

The question you would need to ask is, “If I ask the other guard about which side leads to heaven, what would he answer?”

Let us assume that the door to heaven is on the left.

Let us further assume that the first guard speaks the truth. When you ask him the question, he will say right because he knows that the other guy will lie and will point to hell. In case you asked the liar, he will always point to the hell, as he knows that the other guy will always tell the truth. In fact, you will be directed to hell. So, you will need to go to the door, not explicitly pointed out by any of the guards.

Q – You are driving alone in a car that can accommodate only one more passenger. You find there are three passengers waiting for the bus at a bus stop – an old friend whom you haven’t met for years, a person who you always had wanted as your partner and a lady who needs urgent hospitalization. Who will you take as a co-passenger?

A – Well, that is not seriously a logical question as such. However, this can be the right question that would want to understand your mentality. The ideal answer should be, ‘ I will ask my friend to take the lady to the hospital, and I will wait at the bus stand with the partner of my dreams”. However, answer only if you are convinced! We don’t want to you to cheat your potential employer.

Q – A friend A wants to send a message to friend B – secret info. But, friend B has a friend C whom friend A does not trust and has access to all the mail that friend B receives.  So, he puts the message in a locked box and sends it, but cannot provide the key. How will A send the secret message successfully to friend B?

A – Simple. A sends the box with a lock to B. B receives it and puts another lock and sends it back to A. A will now remove his lock and send it to B. The box now has B’s lock, and he can now easily open it!

Q – Do you have an IQ of more than XXX?

A – This is one of the tricky questions. Once again, you may find it quite a generalized question in all probability. However, this question is primarily asked to test your humility levels.

If you answered YES, that would indeed be a wrong answer. Remembering your IQ or even having to check it indicates that you are a little insecure about your intelligence level.

These few logical interview questions open up your mind, don’t they? They are too interesting and develops your thinking process.

Recommended Reading: What To Write In Subject Line When Emailing Resume For Freshers?

A Few Tricky Questions that Would Rather be Difficult to Answer

Well, while all the above questions are asked to test your job worthiness and thought process, there are a few others that are designed to test you as a human being or perhaps your presence of mind. These can really be quite tricky to answer.

In fact, these tricky questions can be the right options to help you introduce yourself properly for the interview and put a clear indication of your personality.

We will check out a few such questions here –

Q – Would you mind checking your email while on vacation?

A – Well, by all probability, if you are like us, you would not want to be bothered about office work when on vacation. But, you would need to frame your answer in such a way that while you are ready to go that extra mile to get the work done, you also care for your work-life balance. You should frame your answer in such a way that you value the responsibilities while wanting to take care of your personal life as well for better professional growth.

Q – What are your weaknesses?

A – That should be yet another tricky question. You would indeed not want to spoil the possibility of landing into the job by showcasing your weaknesses. But we are humans, and we all have weaknesses. Admit a few if you can recall. But make sure you share them with a silver lining. That would mean you show your willingness to overcome these weaknesses.

Q – Where do you see yourself in the next five years?

A – This question is ideally aimed at testing the candidate’s willingness to stay with the company. Of course, no company will be ready to invest in someone who may not stick around for a more extended period of time. Showcase that you want to grow within your field. Do not be egoistic in your response.

Q – What do you think your references will say about you?

A – This is again a question aimed at testing the insecurity levels that a candidate may have. In fact, it is a trap to make you divulge any of the misgivings you may have with respect to your existing job. Never fall to the trap. However, never be too self-proclaiming either. Stay moderate with your approach and avoid sharing any sort of negative information about your references.

These are a few very commonly asked questions, but not really easy to answer. You have to be very sure about each word you speak. The interviewer shall mark every point you make to drill you during the interview.

The Passing Remarks on Interview Puzzles with Answers

Well, those were a few – just a few puzzles and questions you can expect when attending an interview for a job. In fact, memorizing these questions and answers would not serve you any purpose. Just make sure that the puzzles and questions here in this compilation have been helpful in shaping your reasoning and analytical skills for a better degree of success in the interviews.

The last section may not have any puzzle in the real sense of the word, but that should invariably help you arrive at the best personality while attending the interview. Having a proper understanding of what exactly the interviewer is trying to extract from you can go a long way in helping you achieve the best results.

In essence, the questions here are purely informative in nature and compiled with the aim of inculcating confidence in you by letting you know what the interviewer is attempting to extract from you.