One hundred ants, one meter stick, and a simple rule when they meet. The result seems to depend on everything — positions, directions, collisions — but there is something that remains invariant and simplifies everything.
The stick of a hundred ants
Riddle statement
A straight stick measures 1 meter.
On it there are 100 ants, in any positions.
They all move at 1 centimeter per second.
Each one initially chooses one of the two possible directions along the stick.
When two ants collide, they turn around.
When one reaches an end, it falls.
What is the longest possible time after which you can ensure that the stick is already empty?