Question 31
*Arash* and *Babak* play the following game on a $1400 \times 1401$ table. Starting with *Arash*, he in his turns colors $k$ number of $L$-shaped trominos on the table (rotation and reflection are allowed). Also, *Babak* in his turns colors one $2 \times 2$ square from the table. Every cell of the table can be colored at most once and a player who can not color the cells in his turn will lose. Find all values of $k$ for which *Arash* has a winning strategy.