Some cats got together and decided to kill mice numbering 999919.Each cat kills equal no.of mice and each cat kills more no.of mice than there were cats.Then what is the number of cats?

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- Sep 25th 2008, 09:50 AManand chhetriurgent..cat and mouse
Some cats got together and decided to kill mice numbering 999919.Each cat kills equal no.of mice and each cat kills more no.of mice than there were cats.Then what is the number of cats?

- Sep 25th 2008, 10:23 AMLaurent
You may find useful to know that $\displaystyle 999919=991\times 1009$ where both factors are prime...

- Sep 27th 2008, 11:53 AMnarbe
Dear Friend,

Laurent gives the accurate answer. As an extra explanation we can say :

n(n+b)=999919

where n is number of cats, and b is the difference between number of mice caught by cats and number of cats.

As Laurent said :

(991)(991 + b ) = 999919

b = 18

(991)(991 + 18 ) 999919 (Wink)