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Problem of the Week 900

Friendly Sets

Call a set "friendly" if whenever x is in S, then so is at least one of x-1 and x+1. So {1, 2, 499, 500} is friendly, but {1, 2, 700, 900} is not. How many friendly 5-element subsets of {1,2,3,....899,900} are there?

Source: Bill Sands, Crux Mathematicorum, Nov 1999 25:7 For subscription info regarding this interesting problem journal contact:
© Copyright 1999 Stan Wagon. Reproduced with permission.

30 November 1999