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The plague of mice

The plague of mice

In a certain city, in the face of a brutal plague of mice, cats that each hunted the same number of rodents were used. It is known that 1,111,111 were the hunted mice and less than 1,111 the cats involved. Although there was no physical evidence on the exact number of mice that each cat hunted, this data is recorded in the official records.

How many mice did each cat hunt?

Solution

The only integer divisors of 1,111,111 are 239 and 4649 (1,111,111 = 239 * 4,649). As we are told that we have less than 1,111 cats involved, we will have to 239 cats hunted 4,649 mice each.