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One or Two Fake Coins (Posted on 2005-09-13) Difficulty: 4 of 5
In a group of ten coins there are either one or two fake coins and the rest are real. The fakes can be distinguished from the real coins only by weight. If there are two fake coins they will be equal weights.

Find a strategy to identify the fake coin or coins which uses only a balance scale no more than five times.

No Solution Yet Submitted by Brian Smith    
Rating: 3.6667 (3 votes)

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Some Thoughts A confidence vote | Comment 1 of 4
It is likely it can be done.

If there's only one fake coin, it can be any of the ten, and it can be heavier or lighter, so we have 20 cases.

If there are two fake coins, we have 45 possible pairs, heavier or lighter, giving 90 cases.

The balance can produce three results (left heavier, right heavier, left equals right) so using it 5 times we could have 3^5=243 results.

As 243>90, we should be able to pinpoint the answer.

There remains only a leeeeeeeeeeeetle detail... how to do it! (Details left to the reader.)

  Posted by Federico Kereki on 2005-09-14 02:36:26
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