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Omni-MATH / Let S={1,2,…,9}. Compute the number of functions f:S→S such that, for all s∈S,f(f(f(s)))=s and f(s)−s is not divisible by 3.

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problem

Let S={1,2,…,9}S=\{1,2, \ldots, 9\}. Compute the number of functions f:S→Sf: S \rightarrow S such that, for all s∈S,f(f(f(s)))=ss \in S, f(f(f(s)))=s and f(s)−sf(s)-s is not divisible by 3.
Plain-text mathematical notation (without MathML)
Let S={1,2,…,9}. Compute the number of functions f:S→S such that, for all s∈S,f(f(f(s)))=s and f(s)−s is not divisible by 3.
Original LaTeX notation
Let $S=\{1,2, \ldots, 9\}$. Compute the number of functions $f: S \rightarrow S$ such that, for all $s \in S, f(f(f(s)))=s$ and $f(s)-s$ is not divisible by 3.

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Source and history

task_id
bd535593-d2ee-5119-8bda-e6f6299ecb90
task_key
test--bd535593-d2ee-5119-8bda-e6f6299ecb90
task_revision_id
1
config / split
/ test

Official source

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