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 $Y$.


This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS