Lots of cats and rats

Algebra Level 3

There are \(m\) cats in a rectangular room, where the four corners of the floor have holes. Out of the 1st hole, \(n\) rats come out and each cat eats one rat. The surviving rats scurry back into the hole. Then, twice the number of surviving rats come out of the 2nd hole, again each cat eats one rat, and the surviving rats scurry back into the hole. The process continues for each of the remaining holes.

If the cats again each eat one rat and leave no surviving rats to scurry back to the 4th hole, then what is \(m + n?\)

Assume that \(m\) and \(n\) are coprime.

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