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 Yet one more coin sorting problem (Posted on 2004-05-31)
You have five coins, apparently alike, but actually of different weights. You also have a two arm scale.

Can you manage to sort the coins in ascending order, using the scale only seven times?

Bonus question: can it be done in fewer weighings?

 See The Solution Submitted by Federico Kereki Rating: 4.0000 (4 votes)

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 re(2): yes no maybe | Comment 4 of 20 |
(In reply to re: yes no maybe by Popstar Dave)

With only 128 possibilities to work with and 120 possibilities to distinguish, there's not much inequality of result possibilities that can be allowed in any given weighing.

In weighing B (the heavier of A vs B) against C (the lighter of C vs D), of the 30 possible sequences of weights left after determining B>A and D>C, the two possibilities from step 3 (either B<C or B>C) left only five for the former case (ABCDE, ABCED, ABECD,AEBCD, and EABCD).  That means 25 would remain in the other instance, with only 4 weighings left, capable of distinguishing only 16 cases, so at that point it was hopeless.

Better to weigh A against C (that is, the two lighter weights whichever they are).  Then the 30 possibilities are split evenly 15/15.

 Posted by Charlie on 2004-05-31 10:34:21

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