It seems counterintuitive, but the first three paths are all the same size. If the squares are all unit squares, then the lengths of each of the first 3 paths in 2 units. One way to understand this is that if we have a stair-step pattern made of right-angled turns, then the sum of the lengths of all of the horizontal lines must 1 and the sum of the lengths of all of the vertical lines must 1 -- no matter how many "steps" there are in the path.
The diagonal, on the other hand, is shorter. Its length is the square root of 2 units.
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