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Making The Easy Hard

The Mathematical Miscellany originated in 1836, and was one of the first American mathematical journals. It was not the first, being edged out by the Mathematical Correspondent which started in 1804.

Nonetheless, in The Mathematical Miscellany, the very first problem presented for readers' solution was: "How many diagonals can there be drawn in a polygon of n sides?"

Though quite simple to solve, readers submitted solutions that tended to "reflect" their great mathematical abilities. For example, one of the solutions submitted was by Benjamin Pierce, one of our great American mathematicians. His solution invoked both a finite-difference equation and integration...far beyond what was necessary.

Solution: