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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.
Proposed by Gurgen Asatryan, Armenia



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

Find the greatest


Proposed by Gurgen Asatryan, Armenia
This post has been edited 3 times. Last edited by djmathman, Jun 16, 2020, 4:03 AM
Reason: problem author
Reason: problem author