Difference between revisions of "2001 IMO Shortlist Problems/C1"
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==Problem== | ==Problem== | ||
| − | ''Let <math>A = (a_1, a_2, \ldots, a_{2001})</math> be a sequence 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>'' | + | ''Let <math>A = (a_1, a_2, \ldots, a_{2001})</math> be a sequence 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>.'' |
==Solution== | ==Solution== | ||
Revision as of 16:39, 17 August 2008
Problem
Let 
be a sequence of positive integers. Let 
be the number of 3-element subsequences 
with 
such that 
and 
. Considering all such sequences 
find the greatest value of .
Solution
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