Question 47
There is a bulb in each cell of an $n \times n$ board. Initially all the bulbs are off. If a bulb is touched, that bulb and all the bulbs in the same row and column change state (those that are on, turn off, and those that are off, turn on). Show that it is possible by touching $m$ bulbs to turn all the bulbs on. What is the minimum possible value of $m$?