Tag: The Edge Connection Collection

Three paths to pick from, part 2: Distant connections

~ munizao ~ Leave a comment

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!

Edge Pip Puzzles

~ munizao ~ 1 Comment

Recently* I was perusing the section on edge matching puzzles on Rob’s Puzzle Page. While puzzles using a 3×3 square grid are the most common, one that I found interesting was the 2×3 grid “Matador” puzzle, where matches form dominoes with doubled numbers of pips. Possibly to compensate for the reduction in size, an extra rule requires that not only must edges match, but one match must be present for each pip number between 0 and 6.

My first impulse was to find the simplest complete set that would work as a puzzle. There are 6 different cyclic permutations of a set of four different numbers. Why not try edge-matching with cards using these?

It turns out that this is a pretty easy and not terribly interesting puzzle.

However, in exploring the space of similar puzzles, I found what I think is a particularly elegant gem. If we use cards with edge values between 0 and 8, there are 17 different sums between 0 and 16, which is the same number as the number of internal edges in a 3×4 grid of 12 cards. Coincidentally, 12 is also the number of sets of different numbers between 0 and 8 that sum to 16, so those can be the sets of numbers on our 12 cards.

The last detail is the matter of how we arrange those numbers. Making all of the cards have clockwise ascending edge values is simple enough, although it hurt my symmetry senses to have to pick a direction. And indeed, we don’t have to, because we can make the cards flippable, so that the other sides have values in counterclockwise ascending order. Luckily, the flippable cards are just what the puzzle needed to handle another issue: without them, the puzzle would be unpleasantly hard to solve.

In addition to the collect-all-the sums puzzle, simply matching the numbers makes a good puzzle with this set:

A third challenge is to make a 4×4 square with the corners removed such that every difference between values at the same edge between 1 and 8 occurs exactly twice. I believe I solved this at some point, but I didn’t record the solution, so I can’t show it to you right now.

As you may have noticed, the last puzzle set has higher production quality than the first two. That’s because I’ve had a prototype custom deck of cards made including several different puzzle sets. I intend to have a small run of these made to sell.

*By recently, I mean, whatever was recently last June, when I started writing this post. I don’t mean to only finish blog posts during the earlier part of the year, but it does seem to tend to work out that way.