>>25620960
At first glance, this seems like a losing scenario for the fort, but let’s analyze it carefully.
Each night, 999 rats are killed by the 999 cats.
However, 1000 rats arrive in total, meaning 1 rat survives each night.
Over time, the number of surviving rats will accumulate:
Night 1: 1 rat survives.
Night 2: 2 rats survive.
Night 3: 3 rats survive.
…
Night 999: 999 rats survive.
Night 1000: 1000 rats survive, overwhelming the fort.
After 1000 nights (assuming no changes), the fort is overrun by rats. Despite its seeming impregnability, the slow but constant increase in rats will eventually lead to its downfall. This is a classic case of a slow but inevitable loss due to attrition.