You have five coins, apparently alike, but actually of different weights. You also have a two arm scale.
Can you manage to sort the coins in ascending order, using the scale only seven times?
Bonus question: can it be done in fewer weighings?
The bonus part is easier than the primary question: barring equality of weights (which is valid as they're all "different weights") there are 5! = 120 possible orders for the weights of the coins. Six weighings allows only 2^6 = 64 possible sequences of results of the weighings--not enough to differentiate all the possible orders of weights.
Seven weighings is indeed information-theoretically enough to distinguish 128 possibilities, but actually to set out a methodology in the present case is a different story. It might not be possible.
Posted by Charlie
on 2004-05-31 10:16:07