Art of Problem Solving

1988 USAMO Problems/Problem 3: Difference between revisions

1=2 (talk | contribs)
Created page with "==Problem== Let <math>X</math> be the set <math>\{ 1, 2, \cdots , 20\}</math> and let <math>P</math> be the set of all 9-element subsets of <math>X</math>. Show that for any map ..."
 
Etude (talk | contribs)
No edit summary
 
Line 7: Line 7:
==See Also==
==See Also==
{{USAMO box|year=1988|num-b=2|num-a=4}}
{{USAMO box|year=1988|num-b=2|num-a=4}}
{{MAA Notice}}


[[Category:Olympiad Combinatorics Problems]]
[[Category:Olympiad Combinatorics Problems]]

Latest revision as of 19:44, 3 July 2013

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

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

These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing