In the figure below, if a solution could pass through the top and right sides of the 2, then there must be another solution which is exactly the same except that it passes through the bottom and left sides of the 2, because the squares to the top and right of the 2 are unconstrained (do not contain numbers). Also, the solution must pass through the top-right corner of the 2, otherwise there must be another solution which is exactly the same except that it passes through the top and right sides of the 2.