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?

1st weighing:  1 2 3 4 = 5 6 7 8
2nd weighing:  3 4 5 6 = 1 9 10 11
3rd weighing:  1 5 7 9 = 3 8 11 12

By looking at where each coin is in each weighing, it's easy to deduce the weighing result if that coin is heavier or lighter than the rest.  By tabulating these results, you can easily work the other way (e.g., if the scale tips Left, Right, then Right, your table would show that the counterfeit coin is 5 and it's lighter than the rest.)

Posted by Ken Haley on 2005-06-04 16:01:20