Santa's Little Helpers


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!