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 One of Sixteen (Posted on 2015-12-29)
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)

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 re(3): Short solution. | Comment 11 of 12 |
(In reply to re(2): Short solution. by broll)

I still don't get it.  If your first weighing 6v6 balances what should your procedure be?

If 6v6 balances each side has 2,3, or 4 heavy.
If you take one side and try 3v3 you may still have a problem.
If this balances each side has either 1 or 2 heavy.  Since you don't know which, you can't distinguish with one final weighing.

Wait... I see the way out of this.
The scales can only be equal in the second weighing in the case that the four unweighed coins from the first weighing are all Heavy or all Light.
Take three of these four and weigh versus one of those equal piles of 3.

I don't think you spelled this out.  Is it what you had in mind?  The procedure  doesn't seem complete without it.

 Posted by Jer on 2016-01-12 10:20:32

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