This question is purely a follow-up to Maximum time for ants to fall off stick.
Suppose there are $n$ ants on a stick which has length 10. At any time, the ants may be facing left or right, the initial directions of the ants are arbitrary.
At time 0, all ants start moving in the direction they're facing at speed 1. If an ant reaches the ends of the stick, it falls down (still quite a strange species of ant).
Each time an ant collides with another ant, both ants reverse direction in one unit of time and then continue moving in the new direction.
What is the maximum time an ant can stay on the stick before it falls off?
Clarification regarding ant collisions:
If $X$ encounters $Y$ and $Z$ in the middle of a colliding turn, then $X$ will turn around and leave in 1 time. $Y$ will finish its turn in 0.5 time and then turn around to face $Z$ again. This will take an additional 1 time. $Z$ will finish its turn in 0.5 time and continue on its way.
This makes intuitive sense, by the way, when you remember that $X$ will still be turning when $Y$ finishes its first turn. It couldn't move forward because the path is blocked.
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