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Cell Numbering Sums
Before I started this blog, I explored polyominoes with cells individually labeled with numbers. I called these sumominoes, as I was looking at sets of all polyominoes with a given sum. Erich Friedman...
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Piling Polyominoes
In my previous post I offhandedly tossed off a taxonomy of polyform positioning problems: No OverlapOverlapNo holesTilingPilingHolesPackingTacking The vast majority of the problems you will find in...
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Can 3½ Colors Suffice?
The loan seemed like an incredible break. You got back on top of your mortgage, even had enough to put your oldest into a decent private school. And all they asked you to do was solve puzzles. The...
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Component Colorings
Previously, I looked at problems concerning colorings of individual cells of polyominoes. These were not map coloring problems, (i. e., problems of giving a set of shapes a limited number of colors so...
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Component Colorings II: Diamonds and Triamonds
Here’s a nice coincidence: the numbers of tri-diamonds and di-triamonds are both 9, which is the right amount to tile a regular hexagon of side length 3. And both sets can! Behold the di-triamonds:...
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Extremal Structure-Excluding Polyforms
Here’s a problem that Ed Pegg posted on the Puzzle Fun Facebook group recently: how large can a polyomino be where no line connects four cells? (Diagonal lines in any direction count, and we require...
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Tantalized by Polytans
There are two fundamental methods for deriving a type of polyform. One is to begin with a tessellation, and consider connected subsets of that tessellation as its associated polyforms. The other is to...
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Edgematching to the Stars
The best known combinatorially complete set of edgematching tiles are the 24 squares with 3 edge colors discovered by Percy MacMahon. These can be rotated, but not flipped over. I showed an...
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Three paths to pick from, part 1: A compact gem
I’m going to be sharing a few different puzzles I’ve discovered that share the theme of path building. The first is a pretty polyiamond puzzle I recently prototyped; the other two have been split into...
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Border Marking
This might, at first glance, appear to just be a random tiling of a bunch of dominoes and trominoes. But what would be the point of such a thing? In fact, it’s a complete* set of dominoes and...
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