## Another function on Subsets

Let be the set of all the functions such that for all , we have , where is a finite set (and is the set of its subsets). Find .

*Romanian TST, 2007*

Suppose are the elements subsets of , such that (WLOG).

Then, for any elements () subset of we can write , and by the hypothesis . Therefore, any subset of , different from takes values among .

This means that the image of cannot have more than elements, and we can reach this limit case, by choosing distinct values for .

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Categories: Combinatorics, IMO, Olympiad
IMO, TST

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