You have two ropes and a lighter. Each rope takes exactly 1 hour to burn completely, but they do NOT burn evenly (some parts burn faster than others). How can you measure exactly 45 minutes using these two strings?
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The two ropes
Hints
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- When a rope burns at both ends simultaneously, it burns in HALF the time it would take with just one end.
- String 1 (both ends on): T=30 min: Completely consumed.
- Rope 2 (two-phase strategy): T=45 min: It is completely consumed (30 + 15 minutes).
Solution
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Answer: 45 minutes (30 + 15)
⏱Visual timeline:
String 1 (both ends on):
- T=0 min: Turn on both ends
- T=30 min: It is completely consumed
Rope 2 (two-phase strategy):
- T=0 min: Turn on one end
- T=30 min: Turn on the second end (30 min of rope left)
- T=45 min: It is completely consumed (30 + 15 minutes)
Fundamental physical principle:
When a rope burns at both ends simultaneously,
takes HALF the time it would take with a single end.
Mathematics behind the method:
- Rope 1 at both ends → 60 ÷ 2 = 30 min.
- At 30 min, rope 2 has “half a rope” to burn → light both ends of what remains → 30 ÷ 2 = 15 min.
- Total: 30 + 15 = 45 min.
Why does this method work?
The combustion may be irregular, but the total time of each string is fixed. By lighting at both ends, you create two fire fronts that meet in the middle.
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