11 Apr '05 03:12

Suppose you have 12 coins, 11 of which are identical and one which is fake. The fake coin differs from the 11 others only in that its mass is imperceptibly different (it may be slightly more or slightly less -- you're not sure).

You have a perfectly accurate and sufficiently sensitive balance which can only tell you two pieces of information: 1) whether or not the two sides have equal mass 2) if the two sides do not have equal mass, the balance tells you which side has more mass.

In general, what is the fewest number of times you need to use the balance in order to determine which of the 12 coins is fake?

You are only allowed to use the 12 coins and the balance I have described. You are not allowed to use other weights or balances, to cut coins, etc, etc.

You have a perfectly accurate and sufficiently sensitive balance which can only tell you two pieces of information: 1) whether or not the two sides have equal mass 2) if the two sides do not have equal mass, the balance tells you which side has more mass.

In general, what is the fewest number of times you need to use the balance in order to determine which of the 12 coins is fake?

You are only allowed to use the 12 coins and the balance I have described. You are not allowed to use other weights or balances, to cut coins, etc, etc.