Category Archives: polyominoes

A Case of Accidental Symmetry

The other day I was thinking about putting dominoes onto a 4-by-4 grid without any of the dominoes contacting each others’ sides. I wanted to know how many dominoes you could fit onto the 4-by-4 grid in this way, and … Continue reading

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Latin Squares, Squared Squares, and Legoed Squares

I introduced my kids to Latin Squares the other day. If you know Sudoku then you have seen examples of Latin squares. The idea is to fill in a grid of squares with colors or numbers or some other symbols, … Continue reading

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Proof of radlam Classification

Enough talk, let’s do some math. Sketch of proof of the classification theorem given in The Graph Type of a Polyomino. (I defined radlams in the post Raldams.): First we need some lemmas on how radlams decompose. Lemma 1 (the … Continue reading

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The Graph type of a Polyomino

This is a continuation of the post radlams. A graph is some dots (called nodes or vertices) and lines between some of them (called edges). It’s not the geometry of the graph that matters, just how the vertices are connected … Continue reading

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Radlams

There are five tetrominoes: All but one of them decompose into two dominoes: For the T, no matter which domino you remove, you are left with a pair of monominoes: There are 12 pentominoes: All but one of them decomposes … Continue reading

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