In the famous "The Odd Coin" problem you are given twelve coins, exactly one of which is lighter or heavier than the other coins. You are to determine the counterfeit coin, and whether it is lighter or heavier than the other coins, in just three weighings with a balance.

Can you solve this problem with the additional restriction that you must decide what coins go on each pan for all three weighings before any weighing takes place?

you number the coins 1 -12 . Then you divide the coins into four groups of three.

1,2,3 

4,5,6

7,8,9

10,11,12

Now if you weigh the first group against the second and the third against the fourth you can figure which of the four groups has a light or heavy coin and if it is heavy or light. Now you take that group of coins and weigh one the coins in that group against another one the coins in that group and you can figure out which of the three coins is the heavy or light one. 

Posted by jasper on 2005-06-04 16:08:16