Santa has 1,000 little helpers and a stable with 1,000 stalls. Each stall has a door.

The first little helper puts one reindeer in each stall and shuts __every__ door because
he knows the reindeer will flee to the tundra and gorge themselves on reindeer moss if the
doors are left open too long.

Soon after, the second of Santa's little helpers walks down the stalls and checks every
__second__ door and, finding it closed, opens it.

Almost immediately, the third helper checks every __third__ door; if the door is open he
shuts it and if the door is closed he opens it.

Similarly, the fourth helper checks every __fourth__ door; again, if the door is open he
shuts it and if the door is closed he opens it... and so on.

After all 1,000 helpers have visited the stables, how many reindeer will Santa find in his
stables (*i.e.* how many doors are shut)?

Think about it, try and generalise it to *N* reindeer and, only then, peek at the
Answer!