Overview
This puzzle looks like it needs a simulation — many ants, many collisions, chaotic reversals. It needs one sentence instead.
How to solve Ants on a Stick
- Watch what a collision does to the SET of positions and directions: nothing. Two ants at the same point swap directions, which looks identical to them passing through each other.
- Relabel the ants at every collision so that each label keeps walking straight ahead.
- Under that relabelling nobody ever turns, so each label leaves the stick after at most its full length: 100 cm ÷ 1 cm/s = 100 s.
The key insight
Identity is the red herring. The question asks when the stick is empty, not which ant is where — and 'which ant' is exactly the only thing a collision changes.
Variations & echoes
- The trick generalises to ideal gas particles on a line and to non-crossing lattice paths.
- Ask instead 'which ant falls off which end' and the relabelling no longer helps — that version really does need bookkeeping.
Frequently asked questions
Does it matter how many ants there are?
No. Ten ants or ten thousand, the bound is the same 100 seconds — the time for one ant to walk the whole stick.