Strings of unequal lengths Puzzle

You have these two strings of unequal lengths. They both take exactly one hour to burn from one end to the other when Lighted at any end. But they do not burn at a uniform rate; some sections Burning faster than others and some slower, in a random fashion, which Cannot be predetermined. Any point on either of the strings, However, burns at the same rate forward or backward, whichever end is Lighted. and a match-box. Without any other help, and without Cutting the strings, how would you determine exactly 45 minutes?

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Risihikesh S. Mahajan

Mar 15th, 2005

Follow the steps to find the solution:-1. Take 2 strings as A------------------B C-------------D2. Now as both strings burn in 1 hr. that means if any of them is lit from both ends it will take 1/2 hr. So Lit point A, B and C at a time and start the stopwatch3. After 1/2 hr. string AB will be completely burned. Record this 1/2 hr. Now 2nd string is 1/ 2 burnt i.e it will burn for next 1/2 hr.4. Immediately lit point D. Now as the tring is lit from both the ends and the string is already burnt for 1/2 hr, it will take 15min to burn completely when lit from 2 ends. After burning completely record the time it will be excat 15 min5. Hence 30min(1/2 hr from pt(3)) + 15min (from pt(4)) = 45min...