There are 6 coins weighing 1, 2, 3, 4, 5 and 6 grams that look the same, except for their labels. The labels are supposed to display the weights of the coins.

How can you determine whether all the labels are correct,
using the balance scale only twice?

Let us weigh the coins labeled “1, 2, 3” against the one labeled “6”.
 Iff   balanced the 6 is confirmed. But coins labeled “1, 2, 3” may be permuted and same applies to “4, 5”.

Next   weighing (needed only if 1^st balanced): Weigh coins “1, 6” against coins 3, 5.
Iff  {3, 5} outweighs the pair {1, 6}, all coins are labeled correctly.

Posted by Ady TZIDON on 2016-01-13 17:18:19