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        riddles >> hard >> EXITING A NUMERICAL MAZE
        
(Message started by: pcbouhid on Nov 18^th, 2005, 7:10am)

Title: EXITING A NUMERICAL MAZE
Post by pcbouhid on Nov 18^th, 2005, 7:10am

Note: I´m not achieving a perfect alignment. The moderators can do this? when I make the drawing, the alignment is perfect, but not when I submit the puzzle.

// it took a while to find the right trick, but this seems to do it. --towr

* * * * *
* * * * 4 7 7 * * * *
* * * 5 4 4 8 3 3 4 6 3 * * *
* * 1 4 5 1 1 1 4 5 1 7 1 3 5 * *
* * 4 9 4 9 6 7 5 5 5 8 7 6 6 8 5 * *
* 3 7 2 9 8 3 5 6 7 3 9 1 8 7 5 8 5 *
* * 1 4 7 8 4 2 9 2 7 1 1 8 2 2 7 6 3 * *
* 7 2 1 8 5 5 3 1 1 3 1 3 3 4 2 8 6 1 3 *
* 4 2 6 7 2 5 2 4 2 2 5 4 3 2 8 1 7 7 3 *
* * 4 1 6 5 1 1 1 9 1 4 3 4 4 3 1 9 8 2 7 * *
* 4 3 5 2 3 2 2 3 2 4 2 5 3 5 1 1 3 5 5 3 7 *
* 2 7 1 5 1 1 3 1 5 3 3 2 4 2 3 7 7 5 4 2 7 *
* 2 5 2 2 6 1 2 4 4 6 3 4 1 2 1 2 6 5 1 8 8 *
* * 4 3 7 5 1 9 3 4 4 5 2 9 4 1 9 5 7 4 8 * *
* 4 1 6 7 8 3 4 3 4 1 3 1 2 3 2 3 6 2 4 *
* 7 3 2 6 1 5 3 9 2 3 2 1 5 7 5 8 9 5 4 *
* * 1 6 7 3 4 8 1 2 1 2 1 2 2 8 9 4 1 * *
* 2 5 4 7 8 7 5 6 1 3 5 7 8 7 2 9 3 *
* * 6 5 6 4 6 7 2 5 2 2 6 3 4 7 4 * *
* * 2 3 1 2 3 3 3 2 1 3 2 1 1 * *
* * * 7 4 4 5 7 3 4 4 7 * * *
* * * * 3 3 4 * * * *
* * * * *

Starting from the central cell of this maze (there's a (3) in it), the challenge is to find a path that leads you off the maze, and to a "star" (*).

The number at each cell shows how many steps, in a straight line, you must take. You can travel horizontally, vertically, or diagonally, up or down, left or right.

But! You must reach the first star in the direction you are travelling in an exact number of steps, and not go any further. If you reach a star, and still have some steps "left over", you cannot exit that way.

Title: Re: EXITING A NUMERICAL MAZE
Post by towr on Nov 18^th, 2005, 7:25am

This looks like something most easily done by a computer.

Title: Re: EXITING A NUMERICAL MAZE
Post by pcbouhid on Nov 18^th, 2005, 8:23am

Indeed, towr.

This old puzzle was created by a math puzzlist to show that not all problems can be attacked backwards (what is said to him once). In this one, you don´t know where is the exit.

I use this (I made a board) to use as a game. Each person start at the center with a "colored pin" and, alternating who is in turn to play, each one try to reach the exit first.

Title: Re: EXITING A NUMERICAL MAZE
Post by SMQ on Nov 18^th, 2005, 11:46am

Did somebody say "computer"? ;)

A quick little breadth-first search program found the following two unique solutions: [hide]SW, SW, NE, NE, NE, SW,SW,SW,{NW or SE}[/hide].

-SMQ

Title: Re: EXITING A NUMERICAL MAZE
Post by slapee on Nov 27^th, 2005, 6:34pm

i found a slightly faster way of doing this, but i doubt its the most efficient: [hide]NE, E, S, S, W, S, W[/hide]

Title: Re: EXITING A NUMERICAL MAZE
Post by SMQ on Nov 27^th, 2005, 7:59pm

Unforunately, that doesn't work as you must end on the first star you encounter. Your last step, while it does end on a star, encounters two others first.

--SMQ