Difference between revisions of "2018 IMO Problems/Problem 4"
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Revision as of 00:28, 11 July 2018
Problem 4. A site is any point 
in the plane such that 
and 
are both positive integers less
than or equal to 20.
Initially, each of the 400 sites is unoccupied. Amy and Ben take turns placing stones with Amy
going first. On her turn, Amy places a new red stone on an unoccupied site such that the distance
between any two sites occupied by red stones is not equal to 
. On his turn, Ben places a new blue
stone on any unoccupied site. (A site occupied by a blue stone is allowed to be at any distance from
any other occupied site.) They stop as soon as a player cannot place a stone.
Find the greatest 
such that Amy can ensure that she places at least red stones, no matter
how Ben places his blue stones.
