Two Ropes, Forty-Five Minutes
You have two ropes and a box of matches. Each rope, lit at one end, burns away in exactly 60 minutes.
But the ropes are not uniform. One half might burn away in 50 minutes and the other half in 10. You cannot measure half a rope, or a quarter, or any fraction of it — the only thing you can trust is that a whole rope, lit at one end, takes an hour.
You may light either end of either rope, at any moment.
People usually find 45 minutes first. Work that out, and then push further: what is the shortest stretch of time you can measure with these two ropes?
Answer to type: the shortest interval you can time exactly, in minutes.
💡 I want a nudge
A rope lit at both ends at once is gone in half the time — whatever shape the burning takes.
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Answer: 15
- Light rope A at both ends and rope B at one end, at the same moment.
- Two flames eat rope A from opposite directions and meet somewhere in the middle. Wherever they meet, together they have burned one whole rope — so A disappears after exactly 30 minutes. The unevenness cancels out, which is the whole point.
- At that moment rope B has 30 minutes of burning left in it. Now light B's other end as well.
- B is now burning from both ends with 30 minutes of rope left, so it dies after 15 more minutes. 30 + 15 = 45 minutes from the start.
- And that last stretch — from lighting B's second end to B going out — is itself a measured 15 minutes, the shortest interval these two ropes can give you.
The trick: you cannot measure a piece of the rope, but you can measure a piece of the burning. Two flames on one rope is a way of halving a time without ever knowing where the middle is.