Capgemini Puzzles

Importance of Puzzles in Interviews

A puzzle is a problem or question designed to check how smartly and logically a candidate can think.
To solve a puzzle, you must use logic, reasoning, and sometimes basic mathematics to arrive at the correct answer.
Puzzles help in developing analytical thinking, and people who solve them well are often seen as having strong problem-solving ability and higher cognitive skills.

Why Do Interviewers Ask Puzzles?

Interviewers use puzzle-based questions to evaluate your critical thinking, problem-solving ability, and how you perform under pressure.
These questions test your reasoning, creativity, and ability to think differently when faced with tricky situations.

How to Solve Puzzles in an Interview

Before answering any puzzle, keep these points in mind:

1. Take Your Time

Don’t answer immediately.
Pause, think, and try to understand the puzzle clearly.
If you need more time, politely ask the interviewer.

2. Ask for Clarification

Puzzles can be confusing at first.
If something is unclear, ask questions.
This shows you are serious and attentive, which creates a positive impression.

3. Keep an Open Mind

Think from multiple angles.
Use both standard logic and your own creativity.
The interviewer wants to see how you approach a problem, not just the final answer.

4. Explain Your Thought Process

Whatever answer you give, support it with clear reasoning.
Describe how you interpreted the puzzle, the steps you took, and how you reached the final solution.
This helps the interviewer understand your logical flow.

5. Always Give a Solution

Try to provide an answer, even if you’re not fully sure.
The interviewer is more interested in your approach than whether you are right or wrong.
Not attempting the question may create a negative impression.

Useful Tips

1. Practice Regularly

Solving puzzles daily helps you get familiar with patterns and improves your speed and confidence during interviews.

2. Write Things Down

During the interview, use a pen and paper to jot down points or draw rough ideas.
A visual representation of your reasoning makes your explanation clearer and more effective.

Puzzle 1 :

You have 100 doors in a row, all initially closed. You toggle doors in 100 passes:
– 1st pass: every door
– 2nd pass: every 2nd door
– 3rd pass: every 3rd door
… until the 100th pass.
Which doors remain open at the end?

Explanation:
After completing all passes, only the doors whose numbers are perfect squares remain open.
This is because only perfect squares have an odd number of factors, meaning they are toggled an odd number of times.
Thus, the open doors are:

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100

Question 2

A bag contains 20 blue and 13 red balls. You pick two balls:
– If both are same color → replace with 1 blue ball
– If different colors → replace with 1 red ball
What will be the color of the last remaining ball?

Explanation:
The last ball will always be red.
Reason:
Whenever you pick one red and one blue ball, you put back one red ball, so the count of red balls always stays odd.
An odd number of reds ensures the final ball is red.

Question 3

You stand before 2 doors—one correct, one wrong. One guard always lies, the other always tells the truth. You may ask only one question to each guard. What will you ask?

Explanation:
Ask any guard:
“If I asked the other guard which door is correct, what would he say?”
Both the truthful guard and the lying guard will point to the wrong door.
So, you must choose the opposite door, which is the correct one.

Question 4

Your car tire bursts on a dark road. While replacing it, you lose 4 screws. You have no extra screws. What will you do?

Explanation:
Take 1 screw each from the remaining three tires.
Each tire can safely run on 3 screws.
Install the fourth tire using these 3 screws and drive slowly.

Question 5

100 people are boarding a bus with 100 seats. Person 1 chooses a random seat.
Each next person sits in their own seat if free; otherwise, they pick a random empty seat.
What is the probability that the 100th person gets seat 100?

Explanation:
The probability is ½ (50%).
Ultimately, the last seat depends on whether seat 1 or seat 100 is taken first in the process.
Since both are equally likely, the last passenger has a 50% chance of sitting in seat 100.

Question 6

Three mislabeled boxes contain mangoes, apples, and a mixture. All labels are wrong.
What is the minimum number of boxes you must open to correct all labels?

Explanation:
You only need to open 1 box — the one labeled “Apple + Mango.”
Since the label is wrong, it contains only apples or only mangoes.
Based on what you find inside, you can deduce the correct labels for the other two boxes.

Question 7

Four men A, B, C, and D are buried with only their heads above ground.
They wear 2 black and 2 white hats.
A brick wall blocks A from seeing B, C, or D.
Only one man can deduce his hat’s color. Who is it and why?

Explanation:
C figures out his hat color.
– D sees B and C, but cannot determine his own color.
– A and B see no one.
Since no one speaks, C realizes:
If B and C both had white hats, D would know his own is black and would say so.
Because D is silent, C understands his own hat must be black.

Question 8

Three ants stand on the three corners of an equilateral triangle. Each ant randomly chooses a direction along the edges. What is the probability they do not collide?

Explanation:
They avoid collision only if all ants move clockwise or anti-clockwise.
These are the only 2 collision-free scenarios out of all possibilities.
So probability = 2 possible outcomes / 8 total combinations = 25%.

Question 9

How can you cut a birthday cake into 8 equal pieces with exactly 3 cuts?

Explanation:

Slice the cake horizontally to divide it into two layers.
Slice vertically across the center → now 4 pieces.
Stack the layers and cut once more → gives 8 equal slices.

Question 10

You have 10 stacks of coins. Each correct coin weighs 10 g; one stack contains 9 g coins.
What is the minimum number of weighings needed to find the faulty stack?

Explanation:
You only need 1 weighing.
Take:
– 1 coin from stack 1
– 2 coins from stack 2
– 3 coins from stack 3
… up to 10 coins from stack 10Weigh all 55 coins.
If all were genuine, the weight = 550 g.
Each missing gram tells which stack is faulty:
– 549 g → stack 1
– 548 g → stack 2
And so on.

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