Brainstorming Question Investment Banking

Owner February 1, 2025

Investment banking interviews often include brainteaser questions to assess candidates’ analytical thinking, problem-solving abilities, and composure under pressure. Here are some common brainteasers you might encounter, along with strategies to approach them:

1. The Painted Cube Problem

Question: Imagine a large cube measuring 10x10x10, composed of 1x1x1 smaller cubes. If the entire surface of the large cube is painted, how many of the smaller cubes have paint on them?

Approach:
First, calculate the total number of smaller cubes:
10 × 10 × 10 = 1,000.

Next, determine the number of unpainted interior cubes, which form an 8x8x8 cube:
8 × 8 × 8 = 512.

Subtracting the unpainted cubes from the total gives the number of painted cubes:
1,000 – 512 = 488.

Therefore, 488 smaller cubes have paint on them.

2. The Three-Gallon and Five-Gallon Jug Problem

Question: You have a 3-gallon jug and a 5-gallon jug. How can you measure exactly 4 gallons of water using these two jugs?

Approach:

Fill the 5-gallon jug completely.
Pour water from the 5-gallon jug into the 3-gallon jug until the latter is full, leaving 2 gallons in the 5-gallon jug.
Empty the 3-gallon jug.
Transfer the remaining 2 gallons from the 5-gallon jug to the 3-gallon jug.
Fill the 5-gallon jug again.
Carefully pour water from the 5-gallon jug into the 3-gallon jug until the latter is full.

Since the 3-gallon jug already contains 2 gallons, you’ll add just 1 more gallon to fill it, leaving exactly 4 gallons in the 5-gallon jug.

3. The Bat and Ball Cost Problem

Question: A bat and a ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost?

Approach:
Let the cost of the ball be x dollars. Therefore, the bat costs x + $1. The total cost is given by the equation:
x + (x + $1) = $1.10.

Simplifying:
2x + $1 = $1.10.
Subtracting $1 from both sides:
2x = $0.10.

Dividing both sides by 2:
x = $0.05.

Thus, the ball costs 5 cents, and the bat costs $1.05.

4. The Light Bulb Switch Problem

Question: You are in a room with three light switches, each corresponding to one of three light bulbs in another room. You cannot see the bulbs from where the switches are. How can you determine which switch controls which bulb if you can enter the room with the bulbs only once?

Approach:

Turn on the first switch and leave it on for a few minutes.
Turn it off and immediately turn on the second switch.
Enter the room with the bulbs.

The bulb that is on corresponds to the second switch.
The bulb that is off but warm corresponds to the first switch (since it was recently turned off).
The bulb that is off and cool corresponds to the third switch.

5. The Weighing Coins Problem

Question: You have 10 stacks of coins, each containing 10 coins. All the coins in one of the stacks are counterfeit, and each counterfeit coin weighs 1 gram less than a genuine coin. How can you identify the stack with counterfeit coins using a single weighing on a scale?

Approach:

Label the stacks from 1 to 10.
Take a number of coins from each stack equal to its label number (e.g., 1 coin from stack 1, 2 coins from stack 2, etc.).

In total, you will have 55 coins (1+2+3+…+10).
3. Weigh all 55 coins together.

If all coins were genuine, the total weight would be 55 times the weight of a genuine coin. However, since the counterfeit stack’s coins are lighter, the total weight will be less.

The difference between the expected weight and the actual weight will indicate the number of the counterfeit stack.
For example, if the total weight is 3 grams less than expected, stack 3 contains the counterfeit coins.

Preparation Tips

Practice Regularly: Familiarize yourself with a variety of brainteasers to enhance your problem-solving skills.
Think Aloud: During interviews, articulate your thought process to demonstrate logical reasoning.
Stay Calm: Maintain composure to think clearly and approach each problem methodically.

By practicing these types of brainteasers, you can improve your analytical abilities and perform more effectively in investment banking interviews.