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IfPis a point on a circle, thenP'refers to the diametrically opposite point.

- Arrange the integers from 1 to 1998 uniformly around a circle so that
whenever a+b=a'+b'aandbare adjacent.- How many such "balanced" arrangements of 1, 2, ..., 1998 are there?
Extra credit for enthusiasts:Solve the problem with an arbitrary even integer replacing 1998.

Source:N. J. Finizio and J. T. Lewis, College Math. Journal (25) (Jan 1994) Problem 492, p. 66.© Copyright 1998 Stan Wagon. Reproduced with permission.

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2 October 1998