| Answer
:
The reader is aware
that there are prime numbers
and composite
whole
numbers.
Now, 1,111,111 cannot be a prime number,
because if it were the
only possible answers would be those proposed by Brother Benjamin and
rejected by Father Peter.
Also it cannot have more than two factors, or
the answer would be indeterminate.
As a matter of
fact, 1,111,111
equals
239 x 4649 (both primes), and since each cat killed more mice than
there
were cats, the answer must be 239
cats.
Treated generally,
this problem consists in
finding the
factors, if any,
of numbers of the form (10n
-
1)/9.
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