Solve Maze Without Feedback

Question

Suppose that we have the following maze (_ = open, + = blocked), and we can move left,right,up,down:

+ + + + + + + + + + + + + + + + + + + + + + + + +
+ _ _ _ _ _ _ _ + _ _ _ _ _ _ _ + _ _ _ _ _ _ _ +
+ _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
+ _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
+ _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
+ _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
+ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
+ + + + + + + _ + + + + + + + + + _ + + + + + + +
+ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
+ _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
+ _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ S _ + _ +
+ _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
+ _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
+ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
+ + + + + + + + + + + + + + + + + + + + + + + + +

Given that we start at a random open square in the maze, assuming there is no feedback as to if a move was successful (i.e. we encountered a blocked square) and not knowing where we started, what is a sequence of moves such that we will always end up in the square S.

score 1 · Answer 1 · answered May 08 '19 at 07:53

This question is just a puzzle, so clearly off-topic here, but still it's funny to find answer :-)

For this specific maze there exists sequence of moves that we end up in S.

a) 12*D - and we can end up on top of any +:

 + + + + + + + + + + + + + + + + + + + + + + + + +
 + _ @ @ _ @ @ _ + _ @ @ _ @ @ _ + _ @ @ _ @ @ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + @ @ @ + _ + _ + @ @ @ + _ + _ + @ @ @ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + @ @ @ @ @ @ _ @ @ @ @ @ @ @ @ @ _ @ @ @ @ @ @ +
 + + + + + + + _ + + + + + + + + + _ + + + + + + +
 + _ @ @ _ @ @ _ @ _ @ @ _ @ @ _ @ _ @ @ _ @ @ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ S _ + _ +
 + _ + @ @ @ + _ + _ + @ @ @ + _ + _ + @ @ @ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ @ +
 + + + + + + + + + + + + + + + + + + + + + + + + +

b) 22*L

 + + + + + + + + + + + + + + + + + + + + + + + + +
 + @ _ _ _ _ _ _ + @ _ _ _ _ _ _ + @ _ _ _ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + @ _ _ + _ + _ + @ _ _ + _ + _ + @ _ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + _ + + + + + + + + + _ + + + + + + +
 + @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ S _ + _ +
 + _ + @ _ _ + _ + _ + @ _ _ + _ + _ +@_ _ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + + + + + + + + + + + + + + + + + + +

c) 1*R

 + + + + + + + + + + + + + + + + + + + + + + + + +
 + _ @ _ _ _ _ _ + _ @ _ _ _ _ _ + _ @ _ _ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + _ @ _ + _ + _ + _ @ _ + _ + _ + _ @ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + _ @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + _ + + + + + + + + + _ + + + + + + +
 + _ @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ S _ + _ +
 + _ + _ @ _ + _ + _ + _ @ _ + _ + _ + _ @ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + _ @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + + + + + + + + + + + + + + + + + + +

d) 3*U

 + + + + + + + + + + + + + + + + + + + + + + + + +
 + _ @ _ @ _ _ _ + _ @ _ @ _ _ _ + _ @ _ @ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + _ @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + _ + + + + + + + + + _ + + + + + + +
 + _ @ _ @ _ _ _ _ _ _ _ @ _ _ _ _ _ _ _ @ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ S _ + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + _ @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + + + + + + + + + + + + + + + + + + +

e) 19*L

 + + + + + + + + + + + + + + + + + + + + + + + + +
 + @ _ _ _ _ _ _ + _ _ _ _ _ _ _ + _ _ _ _ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + _ + + + + + + + + + _ + + + + + + +
 + @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + _ + + _ + + _ + _ + + _ + + _ + _ + + _ + + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ S _ + _ +
 + _ + _ _ _ + _ + _ + _ _ _ + _ + _ + _ _ _ + _ +
 + _ + + + + + _ + _ + + + + + _ + _ + + + + + _ +
 + @ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ +
 + + + + + + + + + + + + + + + + + + + + + + + + +

Now it's simple: 5*D, 16*R, 7*D, 5*U, 3*R, 2*D and finish

Solve Maze Without Feedback

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