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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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 What's the problem? (and a spoiler) | Comment 6 of 12 |
Can you clarify the problem, Brian?

I understood the problem to be determining whether one specific coin (call it #1) is heavy or light.

But Broll has solved a different problem, namely finding one coin (not picked in advance) that is known to be either heavy or light.

The easy solution to my problem:
Weighing 1) Weigh 1 vs 2.  If they are different then we are done.  Otherwise, they are known to be equal.

Weighing 2) Weigh 1-2 vs 3-4.  If they are different then we are done, because 1 (and 2) are determined.  Otherwise, all 4 are known to be equal.

Weighing 3) Weigh 1-4 vs 5-8.  If they are different then we are done, because 1-4 are determined.  Otherwise, all 8 are known to be equal.

Weighing 4) Weigh 1-8 vs 9-16.  They must be unequal.  All 16 coins are now determined.

Of course, this process often terminates after 1 weighing (with probability 8/15).

Edited on December 31, 2015, 12:19 pm
 Posted by Steve Herman on 2015-12-31 12:16:44

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