There is a man named Mabu who switches on-off the lights along a corridor at our university. Every
bulb has its own toggle switch that changes the state of the light. If the light is off, pressing the
switch turns it on. Pressing the switch again will turn it off. Initially each bulb is off.
He does a peculiar thing. If there are n bulbs in a corridor, he walks along the corridor back and
forth n times. On the i-th walk, he toggles only the switch whose position is divisible by i. He does
not press any switch when coming back to his initial position. The i-th walk is defined as going
down the corridor (doing his peculiar thing) and coming back again. Determine the final state of the
last bulb. Is it on or off?