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.
(In reply to Short solution.
I don't see how the first part of your solution is guaranteed to work:
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 scales are balanced then the 4 unused coins have either 0,2, or 4 heavy coins. If a 2v2 weighing balances we don't know which case occurred. If the final 1v1 weighing balances we still don't know.
Posted by Jer
on 2016-01-11 12:30:33