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May 12, 2015 at 1:42 comment added AlanZ2223 Say once you take a step down, you cant go up, or versa vise. Also you cannot cross your own path twice
May 11, 2015 at 23:22 comment added M. Wind If you are allowed to visit a location more than once, than the number of paths is unlimited. On the other hand of you can visit a location only once, it is easy to get trapped between your own path and the walls of your area. For example in your picture, go $RDDDLUU$ and you are stuck.
May 11, 2015 at 23:09 vote accept AlanZ2223
May 11, 2015 at 22:48 history edited AlanZ2223 CC BY-SA 3.0
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May 11, 2015 at 22:37 comment added Joffan You seems to implicitly assume that the path is indeed confined to the integer grid lines (despite your mention of "diagonally"). In your example, there are far more than 3 possible paths from x to y, unless there are more constraints you haven't yet explained. For example, starting from x, go down 1, right 2, up 1, left 1, up 1, right 1 to end at y. Is this one of the 3 paths?
May 11, 2015 at 22:30 history edited AlanZ2223 CC BY-SA 3.0
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May 11, 2015 at 22:20 answer added architectpianist timeline score: 0
May 11, 2015 at 22:15 comment added Joffan I'm guessing there must be some constraint on what is meant by a valid path, otherwise there are clearly unlimited possibilities. Is the path confined to the integer grid? Or to line segments joining integer lattice points? Is there some restriction on directions? On revisiting points already part of the path?
S May 11, 2015 at 22:05 history suggested marco11 CC BY-SA 3.0
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May 11, 2015 at 22:02 history asked AlanZ2223 CC BY-SA 3.0