You have 12 coins, six weigh 24 grams and six weigh 25 grams. You also have the broken scale from Five Weights and a Broken Scale.

Sort the 12 coins into the group of 24g coins and the group of 25g coins using that broken scale no more than 9 times.

1) I note that if we balance 6 against 6, the fact that the scale is broken doesn't hurt. If the pans are of unequal weight, then there must be at least two more pounds on one side than the other. In other words, they balance if and only if there are 3 heavy and three light on each side.

2) Situations with 4 coins of 2 heavy and 2 light and 8 coins of 4 and 4 both present the same phenom as seen in (1). If we place all the coins on the scale, they will balance exactly when the weights are equal.

3) I can solve the 4 coin problem in 3 or less weighings. I think there is the possibility that I can reduce the 8 coin problem to the 4 coin problem in 3 moves. If we can reduce the 12 to the 8 in 3 moves, the puzzle is solved in 9 moves. At least that is where my thoughts have led me ...

Posted by owl on 2005-06-30 04:06:21