Knossos Games - Imagine v5:n5

If there is only one lesson that I can give to young puzzle makers, it would be this: Don't force things. Let your puzzles come naturally. If an idea doesn't work right away, set it aside and come back to it later. I have piles of puzzles and half-finished musings that never worked. Puzzles that you would laugh at they're so bad. But all of those constructions have eventually led to some great work (well, at least I think it's pretty good stuff).

This puzzle is a good example of what happens when I don't follow my best piece of advice. In celebration of Imagine's fifth issue in it's fifth volume, I decided that it would be a good idea to make a puzzle that revolved around the number 5. I was running out of time to submit a new puzzle, for it was already late in the spring of 1998, and I needed to make this idea work in a short amount of time. I decided, for lack of a better idea, to recycle an idea that has been done many times before, from two incarnations in Mad Mazes by Robert Abbott (Puzzle 7 - "Jumping Jim" and Puzzle 15 - "Jumping Jim's Encore") to a puzzle printed in Imagine Volume 2 - Number 2 by Tenie Remmel.

While designing the puzzle, I kept track of all the dead ends and loops created in the problem space. After I complete a puzzle, I usually, in a totally separate process, check the problem space for any extraneous solutions I might have missed. But to save some time, I skipped this step, trusting that I had paid close attention to all the possible moves. I submitted the puzzle just before deadline, and the magazine rushed it onto the back cover, without passing it by me for my usual final inspection.

Both cases of cutting corners led to boatloads of trouble. The magazine made a transcription error, and changed one of the numbers in the puzzle. As printed below, the third square in the leftmost column should be a 4 instead of a 2:

The original soultion did not actually use that 4 square, but I'll print it here for comparison:

The 2 allowed for an alternate solution:

But that wasn't the only alternate solution. Even without the transcription error, there was another solution:

And another, ridiculously short solution:

My own carelessness is to blame. There are probably more solutions, and those that I've presented here are courtesy my Math Workshop students from CAA Bethlehem 1998 who took the puzzle out for a test drive. One way to get rid of all of these extraneous solutions is to change the 2 in the fourth square in the second rightmost column to something else, like a 3 (all of the alternate solutions go through that square, but the original solution does not). I admit that I have not charted out all the possibilities for the original puzzle, the puzzle printed in the magazine with the error, or this new solution that I've proposed, so there may be new solutions that I have not considered. However, I wanted to show, to those interested enough, what problems can arise in creating a puzzle, even one as simple as this.

One final note: even though, on the whole, I am thoroughly disappointed with how this puzzle turned out, the zone of fives in the middle is interesting in a mathematical way. The zone of fives essentially creates 25 different pathways through the zone, all accessible via different entrances and exits scattered about the outside edge of the puzzle. This creates a problem space which overlaps itself in a nonphysical way (meaning that it is very un-labyrinth like). If I were to ever make more of these puzzles, they would go in the "Puzzles with Layout" category.