Problem of the Month: Deadline for submission: January 30th, 2006. Extended till February 15th, 2006

Measuring time by burning ropes

You are given an ordinary matchbox and two non-homogeneous non-identical ropes, each of which is known to take exactly one hour to burn from end to end. Question 1 Measure a time period of exactly 45 minutes using only this apparatus. (Note that since the ropes are not homogeneous, you cannot say, for example, that half a rope will take half an hour to burn. For all you know each rope may burn in any random pattern. ) Question 2 Suppose an unlimited number of such ropes and matchboxes is available. What is the set of all the time periods that are measurable? Assume that the inherent capabilities of the apparatus can be used to any extent, disregarding practical constraints. Question 3 Solve Question 2, assuming that a fixed number n of strings is given. Your answer will be a function of n.

Please submit your solutions to courses@isibang.ac.in

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