Suppose that in the world every pair of people either (a) likes one another, (b) dislikes...

Suppose that in the world every pair of people either

(a) likes one another,

(b) dislikes one another, or

(c) is indifferent toward one another.

Prove that in any gathering of 17 people, there is a group of three people all of whom satisfy one of conditions (a), (b) or (c).

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Suppose that in the world every pair of people either (a) likes one another, (b) dislikes...

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