Given a balance scale that is sure to break after X weighings, find an equation for the largest number of coins N, from which you can determine a fake coin that has the wrong weight if

A: You know whether the fake is lighter or heavier

B: You do not know whether the fake is lighter or heavier

(Assume only one of the N coins is fake)

(In reply to re(2): Weighty Solution (maybe!) by Gamer)

Actually, it is quite simple to detect 1 out of 8 coins in 3 weighs.

First divide the 8 coins into 4 pairs A,B,C,D.

Follow the procedure from my first post to find which pair contains the fake (only 2 weighs used so far).

Lastly, use the third weigh to balance either of the coins in the 'fake pair' against any of the six real coins.

If it balances, the untouched coin is the fake; if it doesn't, we know not only that it is the fake but whether it is light or heavy.

BTW, if anyone can direct me to the problem Hank mentioned in which 39 coins can be detected in 4 weighs, I would greatly appreciate it.

Posted by Chris on 2003-05-15 06:43:16