MathDB

In the game "cat and mouse" the cat chases the mouse in either labyrinth

A, B

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)

Problem Statement