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 Mathematical Maze (Posted on 2006-02-28)
You have a checkered board with 7 rows, and 12 columns. You have to move from the top left to the bottom right square. You can only move left, right, up, and down -- not diagonally.

In each row and column, you must step on exactly the number of squares dictated by that row or column. So, because the leftmost column is numbered 1, and you start in the top square of that column, you can never step into that column again. Also, as with all mazes, you cannot cross your own path.

```  1   4   4   1   4   4   7   1   3   7   1   7
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 9
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 7
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 6
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 5
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 7
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 4
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   | 6
+---+---+---+---+---+---+---+---+---+---+---+---+
```

 See The Solution Submitted by Joe Rating: 4.0000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 Solution | Comment 1 of 3
```  1   4   4   1   4   4   7   1   3   7   1   7
+---+---+---+---+---+---+---+---+---+---+---+---+
| > | > | v |   |   | > | v |   | > | > | > | v | 9
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   | v |   | > | ^ | v |   | ^ | < |   | v | 7
+---+---+---+---+---+---+---+---+---+---+---+---+
|   | v | < |   | ^ |   | v |   |   | ^ |   | v | 6
+---+---+---+---+---+---+---+---+---+---+---+---+
|   | v |   |   | ^ |   | v |   |   | ^ |   | v | 5
+---+---+---+---+---+---+---+---+---+---+---+---+
|   | v | > | > | ^ |   | v |   |   | ^ |   | v | 7
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   | v | < |   |   | ^ |   | v | 4
+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   | > | > | > | > | ^ |   | > | 6
+---+---+---+---+---+---+---+---+---+---+---+---+
```

Hopefully that formats correctly. The way I started was to fill in the boxes that you know right off the bat (I just shaded cells on an Excel spreadsheet), for example the upper left corner, and all of the boxes in the three columns labelled with a "7".  Then I worked right to left.

For example, you know you have to end up in the bottom right corner.  Since the column to the left of this is labelled with a "1", you can't cross back once you enter the rightmost column, so you must enter at the top, etc.

The rows labelled "4" and "5" were a big help when working on the left half of the maze, as it limited the possibilities for all of those columns labelled with a "4".  Once you know what some of the boxes *must* be, a little trial and error is all it takes to fill in the rest.

 Posted by tomarken on 2006-02-28 10:32:30

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