Question 5
At the centre of every cell of a rectangular grid $M$ is a point-sized light bulb, initially off. In one turn choose a line passing through no bulb such that all bulbs on one side are off, and switch on all bulbs on that side. At least one bulb must be switched on each turn. Find the largest possible number of turns to switch on all bulbs for:
(a) $21\times21$ cells. (4 points)
(b) $20\times21$ cells. (4 points)
(a) $21\times21$ cells. (4 points)
(b) $20\times21$ cells. (4 points)