Knossos Games - Hexagonal Ordering

I received an e-mail on April Fools day, 2003, asking me to print a puzzle for a magazine similar to Imagine, but for the UK. I have friends that would go to great lengths to pull a prank, and they have the skills to do it right (obtaining the proper e-mail address and domain name, asking just the right questions for such a request, etc...), so I was a bit suspicious at first. Of course, it turned out to be legitimate. Muse is a magazine published by the U.K. National Association for Gifted Children's YouthAgency. Thus, I needed to come up with a new black and white puzzle in short order. The Hexagonal Ordering puzzles fit the bill, in that they are not that difficult to produce, and color is not an essential element of the puzzle or its rules.

If you haven't read the comments posted on the Drawing Boards for Puzzle 1 and Puzzle 2, go back and read them now. There I talk about how the rules of moving from one number to the next make the problem space very modular, which happens again for this puzzle. This puzzle basically has two separate areas, the top portion and the bottom portion, and various decions in one area does not affect decions made in the other. Since you start and finish at the top of the puzzle, early decisions don't affect your progress until the very end of solving the problem. In order to present the problem space in a concise form, I decided to show the problem spaces for the top and bottom portions of the puzzle separately.

Depending upon the decisions made, there are six slightly different ways to reach the number (7,5). Which path you take to get to (7,5), however, won't affect what happens until you return to the top portion of the puzzle. From (7,5), there are basically four different ways to circle around the bottom portion of the puzzle, although only one path succsefully leads you back to the top portion of the puzzle through (3,0). Those six earlier paths are now restricted based on very early decisions, and leaves only one path to the finish.