2003 OIM Problems/Problem 4

Problem

Let $M = {1, 2, \cdots , 49}$ be the set of the first $49$ positive integers. Determine the maximum integer $k$ such that the set $M$ has a subset of $k$ elements in which there are no $6$ consecutive numbers. For that maximum value of $k$ , find the number of subsets of $M$ , of $k$ elements, that have the mentioned property.

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

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2003 OIM Problems/Problem 4

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