{"id":861,"date":"2022-02-07T23:58:05","date_gmt":"2022-02-08T07:58:05","guid":{"rendered":"https:\/\/puzzlezapper.com\/blog\/?p=861"},"modified":"2023-04-07T15:58:51","modified_gmt":"2023-04-07T22:58:51","slug":"the-rune-where-it-happens","status":"publish","type":"post","link":"https:\/\/puzzlezapper.com\/blog\/2022\/02\/the-rune-where-it-happens\/","title":{"rendered":"The Rune Where It Happens"},"content":{"rendered":"\n

A while back, I was finalizing my drawing files for laser-cut frames for my Cross Products<\/a> puzzles, which I was intending to sell at Gathering for Gardner <\/a>13. I wasn’t happy with just wasting the material in the center of the frames, so I looked for a simple idea that would make use of it. The shape that was being cut out was a rectangle with a 3:4 aspect ratio. I could cut that into 12 squares, and then engrave something on each of them. Now what might there be 12 of?<\/p>\n\n\n\n

It will probably not surprise anyone here that my mind went straight to the pentominoes. Tiles with pentominoes could be useful for choosing one at random. (Sure, I already owned a 12-sided die with the pentominoes on it, which I bought from Eric Harshbarger, but with tiles one could select without replacement, or even effectively shuffle an ordering of the entire set.)<\/p>\n\n\n

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The tiles I made for my G4G13 exchange gift didn’t have these fancy swirled colors.<\/figcaption><\/figure><\/div>\n\n\n

The tiles reminded me of rune stones, with the pentominoes forming a cryptic alphabet. I thought it would be amusing to make sets of them my exchange gift for G4G13, along with a slip that instructed the user on how to use the arcane power of the pentominoes to divine the future. It would be the kind of playful deadpan jab at ungrounded mysticism that Gardner’s alter ego, Dr. Matrix, might have enjoyed making. But to really justify the effort, it couldn’t be just<\/em> that. I’d need to include some activity using the pieces that would have genuine recreational math interest. Perhaps a puzzle.<\/p>\n\n\n\n

What I found was a variation on the common superform<\/a> framework that incorporated squares with pentomino runes. The basic common superform problem is to find a figure into which any of the polyforms in a set can be placed. Usually, the object is to minimize the area of such a figure, but in this case, the area will be set by each particular challenge using the pieces. We add a couple of restrictions:<\/p>\n\n\n\n