Ok, another puzzle.
You have a meter stick placed so that the 0cm marker is on the left, and the 100cm marker is on the right.
99 ants are placed on every cm marker from 1 to 99.
The ant at cm 1 is facing to the right. The ant at cm 99 is facing left.
For the 97 ants in between, a coin is flipped to determine if that ant is facing left or right: heads, the ant faces left, tails the ant faces right.
Ants only walk in a straight line at 1cm/s in the direction they are heading. If an ant bumps into another ant, both ants immediately turn around and start walking in the opposite direction.
If an ant walks to either end of the meter stick, it falls off.
1) Prove that, eventually, all ants will fall off?
2) What is the maximum time it will take for all ants to fall off?
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