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Three Tests, Take Three! (Posted on 2005-06-23) Difficulty: 2 of 5
You have nine brass rings, but three are actually gold. Can you pick these out using a balance scale three times at the most?

See The Solution Submitted by Old Original Oskar!    
Rating: 4.0000 (1 votes)

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One Gold Ring | Comment 13 of 14 |

I think that the words 'one of' was left out of the problem statement:
You have nine brass rings, but three are actually gold. Can you pick one of these out using a balance scale three times at the most?

Now, finding one gold ring out of the group is possible in only three weighings.  I will use the fact that gold is heavier than brass.

Make three groups of three: A, B and C.  Weigh A vs B.
If A>B then A must have at least one gold ring.
If A<B then B must have at least one gold ring.
If A=B then C must have at least one gold ring.

Take which group is known to have a gold ring and label the three coins in the group D, E and F.  Weigh D vs E.
If D>E then D is a gold ring.
If D<E then E is a gold ring.
If D=E then weigh D vs F.  If not equal, the heavier is a gold coin; and if equal, all three are gold coins.


  Posted by Brian Smith on 2005-06-27 22:34:17
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