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ring and mice

there is a circular ring in which there are 12 black mice and one white mice.a cat walks circularly in the ring and eats every 12th mice.where should the cat start so that the white mouse is the last one 2 be eaten.
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shilpi84
Asked:
shilpi84
2 Solutions
 
ozoCommented:
The cat should start by eating the mouse 11 before the white mouse
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shilpi84Author Commented:
i knew the answer but cud not figure it out so i would be highly grateful if some1 explains how 2 arrive at this solution.
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Harisha M GCommented:
There are 13 mice in total.

Let them be 1 2 3 4 5 6 7 8 9 10 11 12 13

Now, assume that the cat starts from 1..

Remaining are:
2 3 4 5 6 7 8 9 10 11 12 13

The next one is 13 (12 moves forward)
2 3 4 5 6 7 8 9 10 11 12

Next is 2
3 4 5 6 7 8 9 10 11 12

Next is 4
3 5 6 7 8 9 10 11 12

Next is 7
3 5 6 8 9 10 11 12

Next is 11
3 5 6 8 9 10 12

Next is 8
3 5 6 9 10 12

Next is 6
3 5 9 10 12

Next is 10
3 5 9 12

Next is 9
3 5 12

Next is 5
3 12

Next is 3
12


So, if it eats the first mouse, 12th mouse is the last one to be eaten. So, it should start from the mouse which is 11 position before the required (white) mouse.
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