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Puzzling

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    $\begingroup$ I wonder if there's a way to do this in polynomially many steps. $\endgroup$
    – xnor
    Commented Jul 16, 2015 at 3:55
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    $\begingroup$ Figure out where you are in the maze by simulating making all the moves you've taken so far from the beginning. What exactly do you mean by that and how does this give you an idea of where you are? If I understood the puzzle correctly, the robot does not know the difference between doing and attempting a move (but not moving). So after any amount of steps, it could be anywhere and wouldn't be the wiser, wouldn't it? $\endgroup$
    – BmyGuest
    Commented Jul 16, 2015 at 6:49
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    $\begingroup$ @BmyGuest I believe the intention is 'assume you are in the next maze on the list, then calculate your current position based on the moves made so far' $\endgroup$
    – frodoskywalker
    Commented Jul 16, 2015 at 8:11
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    $\begingroup$ @BMYGuest you don't need to return to your initial position. You maintain a list of all the moves you have made. Then you select a maze that you assume you are in. Then you look at you model of that maze to see where you would be after making all the moves in the list. This puts tells you where you are in the maze if you have made the correct guess about the maze layout. You then find the path from your assumed location to the end, and follow it, adding the moves you make to your list. If you reach the end you are done, otherwise you move on the the next maze. $\endgroup$
    – Taemyr
    Commented Jul 16, 2015 at 9:56
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    $\begingroup$ @xnor A refinement: When conputing the presumtive location see if the path intersects the presumtive exit. If it does then skip the current guess. $\endgroup$
    – Taemyr
    Commented Jul 16, 2015 at 10:14