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2022 SSMO Accuracy Round Problems/Problem 1

Revision as of 12:02, 14 December 2023 by Pinkpig (talk | contribs) (Created page with "==Problem== Consider a bijective function (meaning each element in the domain maps to a distinct element in the range) <math>f:S\rightarrow S,</math> where <math>S=\{1, 2, 3,...")
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Problem

Consider a bijective function (meaning each element in the domain maps to a distinct element in the range) $f:S\rightarrow S,$ where $S=\{1, 2, 3, 4, 5\}$. What is the average of $f(1) + f(2) + f(3)$, over all $f$?

Solution

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