Walk the grid

Discrete Mathematics Level 5

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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