Difference between revisions of "2023 IOQM/Problem 17"

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==Problem==
 
Consider the [[set]]
 
Consider the [[set]]
==Problem==
 
 
<cmath>S = {(a, b, c, d, e) : 0 < a < b < c < d < e < 100}</cmath>
 
<cmath>S = {(a, b, c, d, e) : 0 < a < b < c < d < e < 100}</cmath>
 
where <math>a, b, c, d, e</math> are integers. If <math>D</math> is the [[average]] value of the fourth element of
 
where <math>a, b, c, d, e</math> are integers. If <math>D</math> is the [[average]] value of the fourth element of
 
such a tuple in the [[set]], taken over all the [[elements]] of S, find the largest [[integer]] less
 
such a tuple in the [[set]], taken over all the [[elements]] of S, find the largest [[integer]] less
 
than or equal to D.
 
than or equal to D.

Revision as of 07:11, 20 October 2023

Problem

Consider the set \[S = {(a, b, c, d, e) : 0 < a < b < c < d < e < 100}\] where $a, b, c, d, e$ are integers. If $D$ is the average value of the fourth element of such a tuple in the set, taken over all the elements of S, find the largest integer less than or equal to D.