A set of five coins are of differing weights, no two are equal.

Devise a method to sort the coins by weight using only a balance scale, subject to the restriction that only one coin may be placed on each side in each weighing.

Can this be done in the theoretical minimum of 7 weighings?

This strategy will achieve the theoretical minimum of 7 weighings:

Pick any pair and compare them. Then pick a second pair and compare those as well. Then compare the two heavy coins with the third weighing.

After these three weighings the coins can be labeled A-E such that A>C>D, A>B and E is the unweighed coin.

Use the next two weighings to determine where coin E falls in among A, C, and D. The forth weighing will be E vs C and the fifth will be either E vs A or E vs D depending on the fourth weighing.

At this point the relative weights of A, B, C, and E are known. All that is left is to place coin B. From earlier A>B. Then B can be placed among C, D, and E with two weighings, similar to how E was placed among A, C, and D.

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