Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.
There are cliffs around the island, so he cannot jump off.
How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)
There are 100 bulbs in a room. 100 strangers have been accumulated in the adjacent room. The first one goes and lights up every bulb. The second one goes and switches off all the even-numbered bulbs - second, fourth, sixth... and so on. The third one goes and reverses the current position of every third bulb (third, sixth, ninth? and so on.) i.e. if the bulb is lit, he switches it off and if the bulb is off, he switches it on. All the 100 strangers progress similarly.
After the last person has done what he wanted, which bulbs will be lit and which ones will be switched off?
