Briefly

Uncle Sam's watch chain

Uncle Sam's watch chain


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The other day they showed me a curious watch chain designed according to the old custom of carrying a string of coins attached to a watch.

This particular chain consisted of four coins and the effigy of an eagle.

The coins, as seen in the illustration, respectively had five, four, three and two holes so that the links that linked them could be placed in different ways generating a wide variety of designs.

This peculiarity of being able to produce a series of watch chains with a string of four coins joining the clock with the eagle gave rise to a discussion about the number of different possible arrangements that can be achieved with the five pieces.

What do you think?

Solution

Mathematicians and fans who delight in the mysteries of permutations have calculated that around 92,160 different chains can be made with the four coins and the hanging eagle without two of them being exactly the same.

It is clear that the large coin can be suspended from any of the 5 holes, and with any of the 2 faces facing forward which would admit 10 possible variants.

Since the penny can be placed in 8 positions, these two coins alone would form 80 combinations that multiplied by the 6 positions of the penny and the 4 variants of the other currency and the 2 eagle positions, show that in the order of sizes in the which are now placed there could be 3,840 possibilities.

Since there are 24 variants from the simple variation in the order of the coins 3,840 times 24 days 92,160 combinations as the correct answer to this riddle.



Comments:

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  4. Arashigami

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  6. Dwaine

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