Question 74
Let $k$ and $t$ be integers with $1 \le k/2 \lt t \lt k$. Each square of a $k \times k$ checkerboard is coloured either red or blue. A move consists of choosing a row or a column with at most $t$ red squares and switching the colour of these red squares to blue. Assume that it is possible to make all squares of the checkerboard blue with a sequence of moves, and let $m$ be the least number of moves required to do so. Prove that if $m \gt k$, then the total number of initially red squares is at least $k + 2t$.