On a cliff of length 110m at a height 240m, 10 cats are positioned facing either the left or right direction arbitrarily. The length of the cliff is large compared to the size of each cat. Initially, all cats start running in the direction they are facing at a speed 12m/sec. Whenever any cat collides with another cat, both the cats instantly reverse their respective directions and continue running. When a cat reaches the ends of the cliff, it falls down.on average, how much time does it take for all 10 cats to fall off the cliff?
2026-04-12 11:34:37.1775993677
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Cats on a cliff puzzle
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When placing the cats randomly on the cliff, the randomness balances out to as if you had placed them all in the exact center. Regardless of which direction they face, all of the cats would fall of in $\dfrac{110m}{14m/s} \approx 7.857... $ seconds. I also don't really know what the height of the cliff has to do with the rest of the problem.
Hint: observe that it would take exactly as long if the cats passed by each other without changing directions.