Difference between revisions of "2023 IOQM/Problem 17"
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==Problem== | ==Problem== | ||
Consider the [[set]] | Consider the [[set]] | ||
| − | <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. | ||
![\[S = \{ (a, b, c, d, e) : 0 < a < b < c < d < e < 100 \}\]](http://latex.artofproblemsolving.com/9/1/d/91da1e3305e437df83f9533816d75ca07fb85a22.png)
where 
are integers. If 
is the 
