Difference between revisions of "2016 USAMO Problems/Problem 6"
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Revision as of 14:45, 27 April 2016
Problem
Integers and
are given, with
You play the following game against an evil wizard.
The wizard has cards; for each
there are two cards labeled
Initially, the wizard places all cards face down in a row, in unknown order.
You may repeatedly make moves of the following form: you point to any of the cards. The wizard then turns those cards face up. If any two of the cards match, the game is over and you win. Otherwise, you must look away, while the wizard arbitrarily permutes the
chosen cards and turns them back face-down. Then, it is your turn again.
We say this game is if there exist some positive integer
and some strategy that is guaranteed to win in at most
moves, no matter how the wizard responds.
For which values of and
is the game winnable?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.
See also
2016 USAMO (Problems • Resources) | ||
Preceded by Problem 5 |
Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 | ||
All USAMO Problems and Solutions |