MathDB

Let

M=\{1,2,\dots,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 such that there is no

6

consecutive integers in such subset. For this value of

k

, find the number of subsets of

M

with

k

elements with the given property.

Problem Statement