Bounces among two opposing ant colonies
Question
Alice releases her ants at one end of a thin string and Bob releases his ants at the other end, all walking toward the opposite end. When two ants meet they both reverse direction. How many collisions take place in total?
Short answer
3200. Treat a collision as two ants passing through each other and swapping identities; the set of positions over time is the same. Then every Alice ant meets every Bob ant exactly once and no other meetings occur, giving .
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