### The Devil's Half Doven

In my very first IPP Exchange, in 2000, I presented a puzzle designed by Bill Darrah, called Raft 5. It consisted of 10 sticks, each with a dovetail notch cut across it and a matching dovetail tab glued on along it. There were five different positions on the stick where a notch or tab could be located, for a total of 10 different pieces, and the puzzle contained one of each. Somewhat surprisingly, it's actually possible to assemble these 10 pieces in a raft-like arrangement, with five sticks going one way laid across five going at a right angle.

Raft 5 is a good puzzle, and for the 2003 Exchange in Chicago, I decided to take inspiration from it. The raft is essentially two dimensional, and I wanted to somehow extend the idea into 3-D. To keep the number of possible pieces down, I made my sticks shorter, with only three positions where a notch or tab could be placed, but I also made the sticks square in cross-section (as opposed to rectangular, as in the raft). This allowed tabs and notches to appear on different sides of the stick, even at right angles to one another.

If you leave out the cases where a notch and tab appear in the same position along the stick (unless they're on opposite sides of the stick), then you get a total of 14 possible pieces. That seemed like too many for a good puzzle, so I picked just half of them; I was perversely tickled by the idea of using seven pieces in an interlocking puzzle, instead of the traditional six. Of course, seven pieces can't make a very symmetric shape, but I made a virtue of that, and designed the puzzle so that the final shape isn't particularly important. Instead, the goal is simply to arrange the pieces so that every piece's tab is inserted into some other piece's notch; that forms the pieces into a kind of folded-up loop, each inserted into the next, like a snake eating its own tail.

There are four solutions to the puzzle, two of which have the fun property that the resulting assembly will balance nicely on the end of one of the sticks. Those two solutions look a bit like a figure standing on one foot, which I like quite a lot; at some point, I want to make a very large set of the pieces to use as a bit of artwork for our yard.

## Comments

I got this puzzle recently and I really like it, it is very intriguing. I still haven't figured it out yet. Maybe you could add some runes to give a clue to the solution, sort of like your intriguing puzzle OctaMaze, which I just ordered. I'm really struggling. I figure with the OctaMaze I will have some clues. I wish I wasn't such a puzzle dummy. I never look at the solutions. Should I?

Posted by: John Acord | July 3, 2008 11:25 AM

I agree that, for the great majority of people, this puzzle would be better with little more help to nudge people toward a solution. It'd probably be best for me to find a way to do that without "ruining" it for those crazies who really enjoy the full challenge. Perhaps I'll put together a little "hint trail" of web pages for this puzzle like I did for Octamaze. Good idea, Jon!

On the subject of looking at puzzle solutions, my answer got so long I turned it into a full-fledged blog posting! Check it out via the "Main" link at the top of this page.

Posted by: Pavel | July 3, 2008 11:01 PM