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Equal Sums on a Circle

Place the numbers 1 to 10 around a circle such that the sum of any two
adjacent numbers is equal to the sum of the pair of numbers directly
opposite. In how many ways can this be done? Can this be done with 1 to
8? With 1 to 6?
Source: Based on a problem from
The Little Giant Encyclopedia of Puzzles.

Solution

Mail to Ken