[GGG]

Originally Posted by psyang

I think we have a winner. GGG, I appreciate you walking through your thought process.

Here's the concise solution:

Spoiler!

As GGG discovered, if we assume ants are all identical (indistinguishable from each other) then the puzzle's set up is exactly the same as if the ants just walk past each other instead of reversing direction when they meet.

1) If all ants just walk past each other, they will all walk off the edge.
2) The maximum time (and, indeed, the only time) it takes for all ants to fall off is 99 seconds, the time for ants 1 and 99 (furthest from the edge) to walk the remaining length of the meter stick.

My comments on your solution in bold:

Spoiler!

I quite enjoyed the puzzle and was annoyed at the simplicity and elegance in the end. I was satisfied with my poorly explained intuitive solution about sorting (it works in the symmetrical case and the concept of collisions sort ants work. Essentially it’s similar to ants passing each other means less ant passes until the system is done just much tougher to explain) and was just checking my work for the 5 case when it clicked.