underquark wrote:BUT! What if you have one of the rare - and lighter - 1974 Aluminum ones? Aaprt from it being a Federal Offence to be in possession of one, how can you tell if your pile of 10 has a heavy one or a light one in it?

Ah.... a bit trickier.

[Do they have Pennies instead of Cents in Arizona ?]

But I think you should still be able to do it in 3 weighings.

1.Weigh 3^3

2a If equal

the different coin is in the 4 pile - weigh 3 from the 4 pile against 3 normal coins

-----If equal then the other coin[of the 4] is different

-----If unequal

-----------------If heavier the heavier coin is in the heavy 3 pile -

-----------------If lighter then the lighter coin is in the lighter 3 pile

2b If unequal

compare the heavy pile of 3 with 3 normal ones.

--------------if this equal then the light coin is in the other lighter 3 pile

--------------if this is unequal then the heavy coin is in the heavier 3 pile

3 one more weighing needed in each case

The above logic asumes there is one different coin and nine similar ones. [Uniqueness ?]

What if Hud got it wrong and there was 2 heavy coins and 8 normal ones, how many weighings quarentee identification. ?