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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,© Copyright 1999 Stan Wagon. Reproduced with permission.Crux Mathematicorum, Nov 1999 25:7 For subscription info regarding this interesting problem journal contact: subscriptions@cms.math.ca

30 November 1999