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Home > Logic > Weights and Scales
One of Sixteen (Posted on 2015-12-29) Difficulty: 3 of 5
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.

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Short solution. | Comment 9 of 12 |
(In reply to Short solution. by broll)

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
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