THE GAME OF CATS AND MICE

cat_and_mouse_puzzle
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?
Ob, 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 word ‘mice’.
I can give you just one clue—each cat killed more mice than there were cats.

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JamesBond Pundit Asked on 26th July 2015 in Interview Puzzles.
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  • 2 Answer(s)

    There were 991 cats, and each of them killed 1009 mice.

    To check, 991*1009 = 999919

    Solution:

    Get the prime factorization of 999919
    The prime factors are 991 and 1009 only

    SherlockHolmes Expert Answered on 26th July 2015.
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    Using fermat’s method find the Prime factor.
    Now Let n = 999919 and square root is appx 1000
    so i = 1000 , we find that sqrt(999^-999919)
    = sqrt(81) = 9
    Then 1000 – 9= 991 and 1000+ 9 = 1009
    By multificaton we verify that 991*1009 = 999919
    As Each cat killed more mice than the numebr of cats
    Hence there were 991 cats and each cat killed 1009 mice.

    neha Genius Answered on 26th July 2015.
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