The Puzzle: You have two wires. Each wire takes exactly 60 minutes to burn from one end to the other. However, the wires are non-uniform (one half might burn in 10 minutes and the other in 50 minutes). How can you measure exactly 45 minutes?
1. The Strategy
We need to find a way to make the burn time represent smaller intervals.
Step 1: Measure 30 Minutes
- Lighting a wire from both ends simultaneously will make it burn out in exactly 60/2=30 minutes, regardless of its uniformity.
- Action: Light Wire A at both ends and Wire B at one end.
Step 2: The Final 15 Minutes
- After 30 minutes, Wire A is gone. Wire B has exactly 30 minutes of burn time remaining.
- To measure 15 minutes from that remaining 30, we simply light the other end of Wire B.
- Action: The moment Wire A finishes, light the second end of Wire B.
- When Wire B finishes, exactly 15 more minutes have passed.
2. Total Time
- 30 mins (Wire A) + 15 mins (Remainder of Wire B) = 45 minutes.
Interview-Focused Questions
Q: Why doesn’t the non-uniformity matter?
A: Because even if the wire burns faster at one end, the two flames will always meet when the total remaining mass/length equivalent that takes 60 mins to burn is consumed from both directions. The “midpoint” of time is always reached when you light both ends.
Q: Could you measure 15 minutes using only one wire?
A: No. With only one wire and no clock, you can only measure 30 minutes (by lighting both ends). You need the second wire to “start” the 15-minute countdown from a known 30-minute state.
Key Takeaway
This puzzle tests your ability to use parallelism (both ends) to manipulate a time-based resource.
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