20 Must-Know Math Puzzles for Data Science Interviews: Test Your Problem-Solving Skills

Introduction: 

When preparing for a data science interview, brushing up on your coding and statistical knowledge is crucial—but math puzzles also play a significant role. Many interviewers use puzzles to assess how candidates approach complex problems, test their logical reasoning, and gauge their problem-solving efficiency. These puzzles are often designed to test not only your knowledge of math but also your ability to think critically and creatively.

Here, we've compiled 20 challenging yet exciting math puzzles to help you prepare for data science interviews. We’ll walk you through each puzzle, followed by an explanation of the solution.

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1. The Missing Dollar Puzzle

Puzzle:
Three friends check into a hotel room that costs $30. They each contribute $10. Later, the hotel realizes there was an error and the room actually costs $25. The hotel gives $5 back to the bellboy to return to the friends, but the bellboy, being dishonest, pockets $2 and gives $1 back to each friend. Now, each friend has paid $9 (3 x 9 = 27), and the bellboy kept $2. What happened to the missing $1?

Solution:
There is no missing dollar. The error comes from misinterpreting the situation. The $27 includes the $25 paid to the hotel and the $2 kept by the bellboy.

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2. The Egg Drop Puzzle

Puzzle:
You have 2 eggs and a 100-floor building. You need to find out the highest floor from which you can drop an egg without breaking it. How many drops do you need to guarantee that you find this floor?

Solution:
You can solve this puzzle in a minimum of 14 drops. Start by dropping from the 14th floor, then go up 13 floors if the egg survives, then 12, and so on. This reduces the worst-case number of drops.

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3. The Two Jug Problem

Puzzle:
You have a 3-liter jug and a 5-liter jug, and you need exactly 4 liters of water. How do you measure out exactly 4 liters?

Solution:

1. Fill the 5-liter jug.
2. Pour water from the 5-liter jug into the 3-liter jug until the latter is full. Now, you have exactly 2 liters in the 5-liter jug.
3. Empty the 3-liter jug and pour the remaining 2 liters into it.
4. Fill the 5-liter jug again, and pour water into the 3-liter jug until it is full. Now, the 5-liter jug will contain exactly 4 liters.

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4. The Monty Hall Problem

Puzzle:
You’re on a game show with three doors: behind one door is a car, and behind the other two are goats. After you choose a door, the host (who knows what’s behind each door) opens one of the remaining doors, revealing a goat. Should you stick with your initial choice, or switch to the other unopened door?

Solution:
You should always switch. The probability of winning the car increases to 2/3 if you switch, versus 1/3 if you stick with your original choice.

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5. The Bridge Crossing Puzzle

Puzzle:
Four people need to cross a bridge at night, and they have only one torch. A maximum of two people can cross at a time, and they all walk at different speeds: 1, 2, 5, and 10 minutes. What’s the fastest time they can all get across?

Solution:
The fastest time is 17 minutes. The optimal sequence of crossings is:

1. A and B cross (2 min),
2. A returns (1 min),
3. C and D cross (10 min),
4. B returns (2 min),
5. A and B cross again (2 min).

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6. The 100 Prisoners and Light Bulb Puzzle

Puzzle:
There are 100 prisoners in solitary cells. There’s one light bulb in a central room, initially turned off. The prisoners can’t communicate with each other but are allowed into the room in some random order. They must figure out when all 100 prisoners have visited the room. What’s the strategy to ensure this?

Solution:
Designate one prisoner as the counter. Each time another prisoner enters the room and finds the bulb off, they turn it on if they haven't done so before. The counter increments their count each time they find the light on, then turns it off again. Once the counter reaches 99, they know every prisoner has been in the room.

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7. The Camel and Bananas Puzzle

Puzzle:
A camel has 3000 bananas to transport across a desert, 1000 km wide. The camel can carry only 1000 bananas at a time and eats 1 banana per km. What’s the maximum number of bananas the camel can deliver across the desert?

Solution:
The maximum number of bananas the camel can deliver is 533.33 bananas. The key is to strategically drop bananas along the way and backtrack multiple times.

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8. The Blue-Eyed Island Puzzle

Puzzle:
You’re on an island with 100 people. Some have blue eyes, but they don’t know their own eye color. Every night, if someone discovers they have blue eyes, they must leave the island. One day, an outsider tells the group that at least one person has blue eyes. How long before all the blue-eyed people leave?

Solution:
If there are N people with blue eyes, it will take N days for them all to leave. This is because they will only know they have blue eyes if they don’t see N-1 blue-eyed people leaving.

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9. The Weighing Coin Puzzle

Puzzle:
You have 9 coins, one of which is heavier than the rest. You have a balance scale, and you can only use it twice. How can you find the heavier coin?

Solution:
Divide the coins into 3 groups of 3. Weigh two of the groups. If they balance, the heavier coin is in the third group. Then, weigh two coins from that group to find the heavier one.

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10. The Hourglass Puzzle

Puzzle:
You have two hourglasses: one measures 7 minutes, the other 4 minutes. How do you measure exactly 9 minutes?

Solution:

1. Start both hourglasses at the same time.
2. When the 4-minute hourglass runs out, turn it over (4 minutes elapsed).
3. When the 7-minute hourglass runs out, turn it over (7 minutes elapsed).
4. When the 4-minute hourglass runs out again (8 minutes elapsed), turn it over one last time. When it runs out again, 9 minutes have passed.

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11. The Ant on a Rubber Rope Puzzle

Puzzle:
An ant starts at one end of a 1-meter-long rubber rope, stretching at a rate of 1 meter per second. The ant walks at a constant speed of 1 cm per second. Will the ant ever reach the other end of the rope?

Solution:
Yes, the ant will reach the other end eventually. Although the rope is stretching, the ant makes incremental progress, and the problem can be solved using an infinite series.

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12. The Hats Puzzle

Puzzle:
There are 100 people standing in a line, each wearing either a red or blue hat. No one can see their own hat, but they can see the hats of everyone in front of them. They must guess their hat’s color, starting from the back of the line. How can they maximize the number of correct guesses?

Solution:
The last person in line can announce the parity (even or odd) of the number of red hats they see. Each subsequent person can then use this information and the hats they see to deduce their own hat’s color.

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13. The Rope Burning Puzzle

Puzzle:
You have two ropes, each of which takes exactly 1 hour to burn, but they burn unevenly. How can you measure exactly 45 minutes?

Solution:
Light one rope at both ends and the other at one end. The first rope will take 30 minutes to burn out. At that point, light the other end of the second rope, which will burn in 15 minutes.

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14. The Chessboard and Dominoes Puzzle

Puzzle:
Can you cover an 8x8 chessboard with 31 dominoes, each covering two squares, if two diagonally opposite corners are removed?

Solution:
No, it’s impossible. Removing two opposite corners leaves an unequal number of black and white squares, while each domino always covers one black and one white square.

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Conclusion: Understanding these puzzles not only helps you prepare for data science interviews but also enhances your problem-solving skills. Employers use such problems to test candidates' abilities to think critically, analyze complex situations, and find logical solutions—essential traits for data scientists.

Practice these 20 puzzles, and you’ll feel more confident when facing tricky interview questions.