Every cat killed an equal number of mice

[Q]Question asked by visitor ndk[/q]

A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed one more mice than there were cats.How many cats were there?

sorry visitor i m not satisfied by ur question as
if the no of mice would be 999000.. the no of cats will be 999 and each cat kills 1000 mice i.e (999+1), but in case of ur question its comming out fractional and no of cats cant be fractional

The answer is 991.

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suresh

991*990 = 983072 which is not 999919.

Sultan was right. There is no real solution for the puzzle I can prove it as below.

Let the number of cats be N.

Now, number of mice each cat killed = (999919/N) = N+1 (given)

Or N(N+1)=999919.

N^2+N-999919=0

Now, roots of this equation(I am only considering the +ve root) = -1+(srt(1-4*(-999919)))/2 = 999.45962

So, the answer CAN NOT BE a whole number and there is nothing like a half-cat. So, The puzzle doesn't have a right solution.

-Kalayama

The question should be 'the cats killed more mice than the number of cats' not one more mice.

Then suresh is right.
991*1009=999919