(update: it's amusing how I switched from lemmings to ants in the below without noticing, because I remember this problem told about ants. Won't change it now).

(update: it's amusing how I switched from lemmings to ants in the below without noticing, because I remember this problem told about ants. Won't change it now). Well, you're almost right. The point of this problem is that many people find it quite difficult because they think an ant may "survive" for quite a while on the ledge, getting reflected by other ants. So maybe it starts near the middle, gets reflected soon, then gets reflected again, and who knows how much time it can survive by reflecting off other ants which it directs to the edge during these reflections. Your solution doesn't address this because it only looks at two ants and doesn't explain why couldn't many more other ants make it possible for one ant to survive longer. But actually your solution does contain the crucial insight to solving the puzzle, which is SPOILER SPACE to notice that the reflection doesn't actually do anything. When two ants collide and reflect, we can pretend that they just walked past each other - the movements will be the same and the identities of ants don't matter. If we look at it that way, after 1 minute all ants are off the ledge trivially, as they just keep walking in the same direction. The reason this problem is interesting is that it looks tough before this one insight, and completely trivial afterwards. So the collision rule does add nothing, but not everybody can see that, and that's kinda the point of this puzzle.