1988 USAMO Problems/Problem 3

Problem

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 $Y$ .

Solution

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1988 USAMO (Problems • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5
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1988 USAMO Problems/Problem 3

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