10 Classic Consulting Brain Teasers (with Answers)

While less common than traditional cases, brain teasers still appear in consulting interviews. They test your logical thinking and problem-solving approach.

How to Approach Brain Teasers

1. Don't panic: Take a breath and think before speaking
2. Clarify: Ask questions to understand the problem
3. Think aloud: Share your reasoning process
4. Be structured: Break down the problem logically

Classic Brain Teasers

1. The Light Bulb Problem

You're outside a room with 3 light switches. Inside are 3 light bulbs. You can enter only once. How do you determine which switch controls which bulb?

Solution:

1. Turn switch 1 ON for 5 minutes, then OFF
2. Turn switch 2 ON
3. Enter the room:

- Hot bulb = Switch 1 (was on, now off)

- Lit bulb = Switch 2 (currently on)

- Cold, off bulb = Switch 3

2. The Marble Problem

A jar has 100 marbles: 60 red, 40 blue. Drawing blindly, what's the minimum draws to guarantee 10 of one color?

Solution: 19 marbles

Worst case: You draw 9 red and 9 blue (18 total). The 19th marble must give you 10 of one color.

3. Counterfeit Coin

8 identical coins, one is lighter (counterfeit). Using a balance scale, find it in minimum weighings.

Solution: 2 weighings

1. Weigh 3 vs 3. If balanced, fake is in remaining 2.
2. Weigh 1 vs 1 from the suspect group.

4. The Prisoner Problem

100 prisoners in a row will each receive a hat (black or white). Starting from back, each must guess their own hat color or die. They can see all hats in front but not behind.

Solution: First prisoner counts black hats and says "black" if odd, "white" if even (50% chance of survival). Each subsequent prisoner uses previous answers to deduce their own.

5. River Crossing

A farmer has a fox, chicken, and grain. They must cross a river in a boat that holds only the farmer + 1 item. Fox eats chicken if left alone; chicken eats grain.

Solution:

1. Take chicken across
2. Return alone
3. Take fox across
4. Bring chicken back
5. Take grain across
6. Return alone
7. Take chicken across

Practice Brain Teasers

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Key Takeaways

• Brain teasers test how you think, not just the answer
• Always explain your reasoning
• It's okay to ask clarifying questions
• Practice regularly to build pattern recognition

Ready for more practice? Try our full case math training.