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Yet one more coin sorting problem (Posted on 2004-05-31) Difficulty: 3 of 5
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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Hints/Tips answer to second part | Comment 3 of 20 |

The bonus part is easier than the primary question: barring equality of weights (which is valid as they're all "different weights") there are 5! = 120 possible orders for the weights of the coins.  Six weighings allows only 2^6 = 64 possible sequences of results of the weighings--not enough to differentiate all the possible orders of weights.

Seven weighings is indeed information-theoretically enough to distinguish 128 possibilities, but actually to set out a methodology in the present case is a different story.  It might not be possible.

  Posted by Charlie on 2004-05-31 10:16:07
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