if you have 12 coins, one of which is either heavier or lighter than the others, the others all being the same weight, how can you determine which one it it, and whether it's heavier or lighter, in three weighings.
Well, I did't think about this problem until last weekend when I heard it for a second time. Anyway, it's not too hard to solve, but how about what is the minumum number of weighings that you need to determine which is the odd one, and whether it's heavy or light, from n coins? Eg, you can do 3 coins in 2 weighings, 12 coins in 3, 38 coins in 4 weighings - I'd rather ask for what is the sequence a_n so that a_n is the maximum number of coins such that the odd one can be found (and said to be heavier or lighter). I'd guess this starts 3,12,38... but I can't find this sequence in Sloanes integer sequences, so presumably that means 38 is not the max you can do in 4 weighings... Anyone else tried?