In the game "cat and mouse" the cat chases the mouse in either labyrinth A,B or C .
https://cdn.artofproblemsolving.com/attachments/4/5/429d106736946011f4607cf95956dcb0937c84.png
The cat makes the first move starting at the point marked "K" , moving along a marked line to an adjacent point . The mouse then moves , under the same rules, starting from the point marked "M" . Then the cat moves again, and so on . If, at a point of time , the cat and mouse are at the same point the cat eats the mouse.
Is there available to the cat a strategy which would enable it to catch the mouse , in cases A,B and C?(A. Sosinskiy, Moscow) game strategygamecombinatorics