I have two sets of 8 coins. In one set the coins weigh 30g each, in the other set the coins weigh 31g each.
Unfortunately they got mixed together in one big pile of 16 coins. I want to identify one coin. It can be from either set.

(Easy) Using a balance scale, identify a coin in four weighings.

(Hard) Identify a coin in just three weighings.

Weigh 6v6. If they balance, weigh the other 4 2v2. If they still balance then a final weighing of either side 1v1 will identify a heavy and a light coin. If they don't balance, then both coins in each pan are the same, and we know which.

If the 6v6 don't balance, choose the heavy side, and weigh 3v3. Choose the heavy side again, or either if they balance. Weigh any two of these coins. If they balance, both are heavy. If they don't then they must be light and heavy, and we know which.

The detailed proof is straightforward and is left as an exercise for the reader.

 

Edited on December 30, 2015, 10:24 pm

Posted by broll on 2015-12-30 22:09:31