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