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Devilish Difference (Posted on 2005-08-22) Difficulty: 3 of 5
Suppose you select 501 numbers from 1 to 1000, inclusive. Show that if no two of the selected numbers differ by 334, then some two of the selected numbers differ by 666.

See The Solution Submitted by McWorter    
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Some Thoughts re(2): Solution | Comment 5 of 6 |
(In reply to re: Solution by McWorter)

Why, thanks! Looking back at my solution, I realized that it works not only for 334 and 666, but for any pair of numbers whose sum is not greater than 1000.
  Posted by Federico Kereki on 2005-08-23 19:53:04

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