I promised two more path puzzles in part 1, and their time has come. When I posted recently about “starmaps” as a variation on edgematching puzzles, my variation there was actually the second puzzle inspired by them that I had found recently. The first was this set of 2×2 square tiles with one cell being marked with 2 orthogonal or diagonal arrows. (The tiles can be flipped.)

Part of the inspiration to use arrows may have come from the game of Trippples, [siccc] which uses a complete set of fixed square pieces with arrows in three directions. I recently read about Trippples in issue 7 of Abstract Games magazine. Once I had these squares with arrows, a puzzle challenge seemed natural: connect the arrows into a single path, which may not enter any cell with arrows in any direction that does not correspond to an arrow.

Problem 61: Find a closed circuit using these pieces. I spent enough time finding the path above; I suspect that a closed circuit may be solvable if you have the patience of a Lewis Patterson, which I do not.

One element I like to consider in puzzle design is non-locality. A puzzle exhibits non-locality if, when you are placing a piece, you must consider pieces that are not immediately adjacent. Most polyform and edgematching puzzles are generally local. If half of a puzzle frame is filled, pieces in the interior of the filled region do not directly affect how new pieces can connect to the edge of that region. (Of course, I am eliding the fact that they reduce the set of remaining pieces that are available to place.) In the above puzzle, the empty space allows long distance connections, turning path-making into a non-local problem.

My Color Tubes puzzle from my Edge Collection Connection set of edgematching card puzzles was also a path puzzle with non-local considerations. I neglected to introduce it on the blog back when I produced the set, so let’s remedy that now.

The configuration shown is a solution to the challenge of placing the pieces so that each tube has three segments of three different colors. Segments can break in the middle of a card, or at a connection across a card boundary with non-matching colors. (Here, the cards cannot be flipped over; the back sides of the cards contain a second, related puzzle.) Other challenges for the cards are placing them so there are two differently colored segments, or four. This was definitely more of a “designed” puzzle than a “discovered” puzzle, which was a bit of a departure for me. I’ll have another excuse to muse about the distinction in a future post, but at this point I’ve hinted at more than one future post, so they can’t all be the next one.

With a couple of instances of non-locality under our belts, can we say anything useful about it as a puzzle design tool? In the case of Color Tubes, I think it gives it a little more depth than a typical 3×3 edgematching puzzle, which would seem to be welcome. In the arrow path puzzle, it adds difficulty and complexity, but the result is a little too much difficulty and complexity, at least for my tastes. It is a spice that should be judiciously applied. But then, so is hinting at coming posts, and that won’t stop me from teasing more material about non-local puzzles in the near future!