Difference between revisions of "2001 IMO Shortlist Problems/C1"

(New page: ==Problem== ''This problem has not been edited in. If you know this problem, please help us out by <span class="plainlinks">[{{fullurl:{{FULLPAGENAME}}|action=edit}} adding it]</span>.'' ...)
 
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==Problem==
 
==Problem==
''This problem has not been edited in. If you know this problem, please help us out by <span class="plainlinks">[{{fullurl:{{FULLPAGENAME}}|action=edit}} adding it]</span>.''
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''Let <math>A = (a_1, a_2, \ldots, a_2001)</math> be a sewuence of positive integers. Let <math>m</math> be the number of 3-element subsequences <math>(a_i, a_j, a_k)</math> with <math>1 \le i < j < k \le 2001</math> such that <math>a_j = a_i + 1</math> and <math>a_k = a_j + 1</math>. Considering all such sequences <math>A</math> find the greatest value of <math>m</math>''
<includeonly>[[Category:Problems needed]]</includeonly>
 
  
 
==Solution==
 
==Solution==

Revision as of 15:37, 17 August 2008

Problem

Let $A = (a_1, a_2, \ldots, a_2001)$ be a sewuence of positive integers. Let $m$ be the number of 3-element subsequences $(a_i, a_j, a_k)$ with $1 \le i < j < k \le 2001$ such that $a_j = a_i + 1$ and $a_k = a_j + 1$. Considering all such sequences $A$ find the greatest value of $m$

Solution

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