4by12

Ants on a Stick

You have a 1 meter long stick and 100 ants. The ants are somehow distributed on the stick, and each ant moves either right or left at 1 meter/second. When two ants meet, they both instantaneously turn around and start walking in opposite directions, still at 1 meter/second. When an ant reaches the edge of the stick, it falls off.

If you control the initial placement and movement directions of the ants, what is the longest an ant can remain on the stick?

The answer: An ant can stay on the stick for at most one second.

The given situation is that when two ants meet, they both turn around and start walking in opposite directions. But this is exactly the same as a situation where the ants never interact, so when they meet they just pass through one another and continue walking in their original directions.

An single ant will remain the longest on the stick if you place it at one edge of the stick and let it walk towards the other edge. This will take exactly 1 second. And because the ants are indepedent, this is also the answer for 100 ants.