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Omni-MATH / Two players, B and R , play the following game on an infinite grid of unit squares, all initially colored white. The players take turns starting with B . On B 's turn, B selects on…

Problem

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problem

Two players, BB and RR , play the following game on an infinite grid of unit squares, all initially colored white. The players take turns starting with BB . On BB 's turn, BB selects one white unit square and colors it blue. On RR 's turn, RR selects two white unit squares and colors them red. The players alternate until BB decides to end the game. At this point, BB gets a score, given by the number of unit squares in the largest (in terms of area) simple polygon containing only blue unit squares. What is the largest score BB can guarantee? (A simple polygon is a polygon (not necessarily convex) that does not intersect itself and has no holes.)
Plain-text mathematical notation (without MathML)
Two players, B and R , play the following game on an infinite grid of unit squares, all initially colored white. The players take turns starting with B . On B 's turn, B selects one white unit square and colors it blue. On R 's turn, R selects two white unit squares and colors them red. The players alternate until B decides to end the game. At this point, B gets a score, given by the number of unit squares in the largest (in terms of area) simple polygon containing only blue unit squares. What is the largest score B can guarantee?
(A simple polygon is a polygon (not necessarily convex) that does not intersect itself and has no holes.)
Original LaTeX notation
Two players, $B$ and $R$ , play the following game on an infinite grid of unit squares, all initially colored white. The players take turns starting with $B$ . On $B$ 's turn, $B$ selects one white unit square and colors it blue. On $R$ 's turn, $R$ selects two white unit squares and colors them red. The players alternate until $B$ decides to end the game. At this point, $B$ gets a score, given by the number of unit squares in the largest (in terms of area) simple polygon containing only blue unit squares. What is the largest score $B$ can guarantee?
(A simple polygon is a polygon (not necessarily convex) that does not intersect itself and has no holes.)

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Source and history

task_id
7788144b-bf07-57ed-bcd7-37616dca3884
task_key
test--7788144b-bf07-57ed-bcd7-37616dca3884
task_revision_id
1
config / split
/ test

Official source

initial import