1988 USAMO Problems/Problem 3


Let $X$ be the set $\{ 1, 2, \cdots , 20\}$ and let $P$ be the set of all 9-element subsets of $X$. Show that for any map $f: P\mapsto X$ we can find a 10-element subset $Y$ of $X$, such that $f(Y-\{k\})\neq k$ for any $k$ in $Y$.


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See Also

1988 USAMO (ProblemsResources)
Preceded by
Problem 2
Followed by
Problem 4
1 2 3 4 5
All USAMO Problems and Solutions

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