Ants on a ruler

♠ Posted by GeekyFry in , at 10:09 AM

A group of N ants fall at the same time on a ruler with a length of L centimeters. Each ant lands on a random spot along the ruler (but none of them miss the ruler).
After landing (and recall that each ant lands on the ruler at the same time) each ant starts moving along the ruler to either the left or the right (the decision is random).

The ant’s velocity is a constant 1-centimeter per minute.
When an ant walking in one direction hits another ant walking in the other direction, they BOTH turn (the turn is at zero time) and start walking in the opposite direction.
When an ant reaches the edge of the ruler, it falls.
Here’s the question:
According to the conditions above, what is the time limit for the ruler to be free from ants?


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