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Here is a seemingly simple physics problem but is a hard nut To crack. there is a balloon with mass m attached to it. It Is descending with an acceleration a. How much amount of mass should Be removed from the balloon so that it rises with an Acceleration a assuming that there is negligible change in the volume of the Balloon when the mass is removed?

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You and i each have two prime numbers on our foreheads And are told that any three of them form the sides of a triangle With prime perimeter. we take turns stating whether we can deduce the Numbers on our own foreheads. You see 13 and 17 on my forehead and each of us has stated "don't know" on each of our first two turns. It is now Your third turn. what are the numbers on your forehead? 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?