## Random Walk

There were a couple of puzzles during the MIT Mystery Hunt that were not so mysterious. Unlike in traditional hunt puzzles, these puzzles were accompanied by instructions. As a result you can dive in and just enjoy solving the logic part of the puzzle without bothering about the final phase, called the extraction, where you need to produce the answer.

The first puzzle with instructions is Random Walk by Jeremy Sawicki. I greatly enjoyed solving it. In each maze, the goal is to find a path from start to finish, moving horizontally and vertically from one square to the next. The numbers indicate how many squares in each row and column the path passes through. There are nine mazes in the puzzle of increasing difficulty. I am copying here two such mazes: the easiest and the toughest. The colored polyomino shapes are needed for the extraction, so you can ignore them here.

1. #### Alexander:

Can you pass through the same square multiple times? If so, is it counted that many times or only once?

2. #### Alexander:

^After solving the first one, it’s not required, so I guess it’s not permitted.

I wonder if there would be multiple solutions if it was.

3. #### Tanya Khovanova:

You can’t pass through the same square twice. There is an example in the original puzzle, if you follow the link.

4. #### fibonicci:

there can be multiple path for same square.

5. #### Tanya Khovanova:

Each solution is unique.