Classic warm-up puzzle.
Two ropes, forty five minutes
The question
Two ropes each burn for exactly one hour but not at a uniform rate. Using only these, measure forty five minutes.
Have a go before you open the solution. If you are stuck after a few minutes, the first paragraph below is usually enough of a nudge.
Show the worked solution
The answer
Light rope A at both ends and rope B at one end. When A finishes, light B's other end.
Rope A lit at both ends burns out in thirty minutes regardless of how uneven it is, because the two flames together consume the whole rope.
At that moment rope B has thirty minutes of material left, burning from one end.
Lighting B's second end halves that remaining time to fifteen minutes.
Thirty plus fifteen is forty five. The key idea is that burning from both ends halves whatever time remains, which is a tool you can reuse rather than a trick.
What it is testing
Whether you can find an invariant when the obvious measurement is unavailable.
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