2021 Iran MO (3rd Round)

Part of Iran MO (3rd Round)

Subcontests

(4)

1

Arash and Babak L-corners squares

Arash and Babak play the following game, taking turns alternatively, on a

1400\times 1401

table. Arash starts and in his turns he colors

k

L

-corners (any three cell of a square). Babak in his turn colors one

2\times 2

square. Neither player is allowed to recolor any cell. Find all positive integers

k

for which Arash has a winning strategy.

4

5

4