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 20050630 04:06:21 