Problem of the Week 948

A Lottery Anomaly

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Consider a lottery where six numbers are chosen randomly from {1, 2, ..., M}. What is the largest value of M so that it is more likely than not that the chosen set has two consecutive integers?

Notes: You may have noticed this consecutive-number phenomenon in the winning 6-tuples of real lotteries. The numbers are chosen without replacement; they are presented in sorted order (i.e., order is irrelevant).

Source: David Berman, College Math. Journal, Jan 1994.

© Copyright 2001 Stan Wagon. Reproduced with permission.