Q: You have two ropes that each take one hour to burn, but they burn at inconsistent rates. How can you measure 45 minutes?

Solution:

1. Light both ends of rope A and one end of rope B
2. When rope A burns out (30 mins), light other end of rope B
3. Rope B will burn remaining 15 mins

Key Skills Demonstrated:

• Creative thinking
• Time management
• Problem decomposition

3. Probability Questions

Q: You have 3 ants on three corners of a triangle. Each ant randomly picks a direction and starts walking along the edge. What’s the probability they don’t collide?

Solution:

• Only 2 of 8 possible combinations avoid collision
• Probability = 2/8 = 1/4 = 25%

4. Sequential Reasoning

Q: What’s the next number in the sequence: 2, 6, 12, 20, 30, ?

Solution:

• Pattern: Add 4, then 6, then 8, then 10
• Next number: 42

5. Visual Puzzles

Q: What has a head and a tail but no body?

Answer: A coin

What It Tests:

• Lateral thinking
• Ability to consider multiple perspectives

6. Mathematical Logic

Q: If five cats catch five mice in five minutes, how many cats would you need to catch 100 mice in 100 minutes?

Solution:

1. Analyze the ratios:
   
   • 5 cats : 5 mice : 5 minutes
   • Rate is 1 mouse per cat per minute
2. For 100 mice in 100 minutes: Still need 5 cats

7. Process Questions

Q: How would you move Mount Fuji?

Approach Example:

1. Define requirements
2. Consider methods:
   
   • Physical removal
   • Digital recreation
   • Symbolic movement
3. Evaluate feasibility
4. Present recommendations

8. Estimation Challenges

Q: How many windows are in New York City?

Structured Approach:

1. Break down building types:
   
   • Residential
   • Commercial
   • Industrial
2. Estimate numbers per category
3. Show multiplication process