You have 2 pieces of rope, each of which burns from one end to the other in 30 minutes (no matter which end is lit). If different pieces touch, the flame will transfer from one to the other. You cannot assume any rope properties that were not stated. Given only 1 match, can you time 45 minutes?
Take one rope (Rope A), place it down as a circle. Light match and start burning rope A at the tips that are touching. When the rope completely burns out, 15 minutes will have passed (since both ends are burning and being consumed at once). Hold the second rope (Rope B) straight and place one end so that it will immediately catch fire when the two burning points from (Rope A) finally touch and are just about to burn out.
Thus 15 minutes on Rope A + 30 minutes on Rope B gives you 45 mins.
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