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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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solution | Comment 3 of 5 |
There are a total of 12 chairs, and only 9 people. That leaves us 3 empty seats. That means that we can have, at most, 4 groups being seated.

There are 9 people amongst 4 groups, and 9 / 4 = 2.25, which is the average group size in this configuration.

Since our average is greater than 2, that is, 2.25 > 2, at least one set of occupied chairs will have 3 or more people seated in a row.

  Posted by Justin on 2010-09-14 13:28:23
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