Board Meeting

Prove that if seven darts land on a dartboard, there will always be two darts that are no farther apart than the distance of one radius.

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Image: Wikimedia Commons Divide the dartboard into six equal sectors. One of these must contain at least two of the darts, and these two cannot be farther apart than the length of a radius. Interestingly the same conclusion can be reached even if only six darts are thrown — see Tony Crilly and Stephen Suen, “An Improbable Game of Darts,” Mathematical Gazette 71:456 [June 1987], 97-100.