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Catch The Mice

The cat must go round and round the circle, in the direction that you are looking, and eat every thirteenth mouse.
The cat must keep the white mouse for a tit-bit at the finish. 
At which mouse should the cat start the count in order that the white mouse be the last eaten?
What is the smallest number that the cat can count round and round the circle, if he must start at the white mouse (calling that "one" in the count) and still eat the white mouse last of all?
What is the smallest number that the cat can count round and round if she must start at the white mouse (calling that "one") and make the white mouse the third eaten?

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Math Genius