MathDB

4

Part of 2023 USAJMO

Problems(1)

B and R color squares Blue and Red

Source: USAJMO 2023/4

3/23/2023
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.)
Proposed by David Torres
hard