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2002 OIM Problems/Problem 4

Revision as of 16:37, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>M = {1, 2, \cdots , 49}</math> be the set of the first <math>49</math> positive integers. Determine the maximum integer <math>k</math> such that the se...")
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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

Solution

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See also

https://www.oma.org.ar/enunciados/ibe18.htm

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