Functions With Exactly One Inverse Condition

2175ExpertCombinatoricsFunctions

Harvard-MIT Mathematics Tournament

For what positive integers $n$ do there exist functions $f, g:\{1,2, \ldots, n\} \rightarrow \{1,2, \ldots, n\}$ such that for each $1 \leq i \leq n$, either $f(g(i))=i$ or $g(f(i))=i$, but not both?

0 students attempted0% solvedRating 2175

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Functions With Exactly One Inverse Condition

2175ExpertCombinatoricsFunctions

Harvard-MIT Mathematics Tournament

For what positive integers $n$ do there exist functions $f, g:\{1,2, \ldots, n\} \rightarrow \{1,2, \ldots, n\}$ such that for each $1 \leq i \leq n$, either $f(g(i))=i$ or $g(f(i))=i$, but not both?

0 students attempted0% solvedRating 2175