You are extremely sick and there is only one way to save your life. A king offers you 12 pills but only one of them will cure you. 11 of the pills are lethal and there is 1 that is good. However, all 12 pills are identical in every way except for their weight. The 11 leathal pills all weigh the same, but the 1 good pill either weighs more or less than the others. The king only gives you one balance scale to figure this out and you only get three attempts to measure the pills to discover which one is the good one. Please tell me the process you take in order to figure out which pill is the good one.

Asked and answered, as the lawyers say.

Detailed proof for N=12. General theorem for any N (unproven in the forum)

I give a different solution in which weighings are unconditional (i.e. don't depend on previous weighings) inhttp://wilmott.com/310/messageview.cfm?catid=15&threadid=5185&highlight_key=yIn that solution you weigh 4 against 4 each time. However this solution is a sort of "guess". I have no idea how to approach the general problem. Does anyone know by the way if it's the famous Besikovich solution the general coins problem (which was according to some source taking so many mathematicians man hours during the war that it was suggested to drop it on germans?)You see, in the "true" version those are neither pills nor balls, but coins By the way, it is easy to get a lower bound of log(2N)/log(3) by primitive "information theory" arguments, which I describe in my solution for N=12. That's close to the actual answer log(2N+3)/log(3) stated by Chukcha.