# Walk the grid

You start at the point $$(x,y) = (1,1)$$ in a Cartesian coordinate system.

Every second you move randomly 1 unit either up, down, left or right.

What is the expected value for the number of seconds it will take for you to land on a point $$(5m, 5n)$$ where $$m$$ and $$n$$ are integers?

Clarification: You can walk anywhere in all four quadrants of the Cartesian coordinate system. $$m$$ and/or $$n$$ can be negative.

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