Home > Riddles > The palo of the hundred hormigas
One of the best identity swap pieces: crashes seem to complicate everything, but they don't really change anything that matters.
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 extreme, one falls.
What is the longest possible time after which you can ensure that the stick is empty?
The key idea is that, to know when the stick is empty, it is not important to distinguish some ants from others. When two identical ants collide and turn around, the overall effect is indistinguishable from one in which they simply pass each other and continue straight.
So the problem can be thought of in a much simpler way: 100 ants that do not interact; each one continues in a straight line until falling at one end. In that version, the one that may take the longest is an ant located at an unfavorable end, which has to travel the entire meter at 1 centimeter per second.
That's 100 centimeters / 1 centimeter per second = 100 seconds.
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