Measure 75 minutes with three uneven ropes

Question

A proctor must time an exam that lasts exactly 75 minutes and has only a box of fuses and a lighter. Each fuse (rope) takes exactly 60 minutes to burn from one end to the other, but the ropes are non-uniform, a rope that looks half gone has not necessarily burned for 30 minutes. You may light any end of any rope at any moment. Using three such ropes and the lighter, measure exactly 75 minutes.

Accepted Answer

The one tool you have is: lighting a rope at both ends burns it out in exactly 30 minutes, no matter how uneven it is, because the two flames together consume the whole "60 minutes of material" and meet after 60/2 = 30 minutes. Build 75 minutes as 45 + 30. 1. At time 0, light Rope A at both ends and, at the same moment, light Rope B at one end. The exam begins. 2. At time 30, Rope A is fully consumed. Rope B has been burning from one end for 30 minutes, so it has 30 minutes of material left. Immediately light Rope B's other end too. With 30 minutes of material now burning from both ends, it w…

Measure 75 minutes with three uneven ropes

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