The Game of Cats and Mice

           A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice.

           How many cats do you think there were? 

           Oh, by the way let me clarify just two points- it is not one cat killed the lot, because I have said ‘ Cats’ and it is not 999919 cats each killed one mouse, because I have used the words ‘ mice’

I can give you just one clue – each cat killed more mice than there were cats.

Answer:  Just one look at the number 999919 and we know that it cannot be a prime number. And if the problem has to have only one answer, this number can have only two factors. The factors are 991 and 1009, both of which are primers. 

              We know that each cat killed more mice than there were cats, and therefore, the correct answer clearly is that 991 cats killed 1009 mice.