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12 chairs (Posted on 2010-09-14) Difficulty: 1 of 5
If 9 people are seated in a row of 12 chairs, then at least one consecutive set of 3 chairs is occupied by people.

Prove it.

See The Solution Submitted by Ady TZIDON    
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Sparseness | Comment 1 of 5
The most sparse set containing three empty chairs ("E") would appear to be SS E SS E SS E SS (11 chairs, 8 seated).  If any of the three E were adjacent, the set would be shorter; if any of the seated ("S") were longer, the condition would have been satisfied.  This seems obvious, but I do not know just what would count as a "proof".  One could, of course, show all possible configurations or 9 S and 3 E -- that of course would prove the assumption. 
  Posted by ed bottemiller on 2010-09-14 12:16:59
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