iiinova — where your digital self keeps evolving

Alexandre Muñiz @two-star.bsky.social · 04/09/2026

Yay, we're doing quizzes. Welcome to LiveJournal! I think the little Midwestern I have in my PNW English comes from my mom via my grandpa. But there are quirks in my idiolect that the quiz doesn't catch, like the middle syllable in "tomato" rhymes with hat, and "cómoda" instead of dresser.

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Alexandre Muñiz @two-star.bsky.social · 25/08/2026

There are 6 ways to place 1 | and 1 – stripe on L4 through cell centers. For Z4, there are 3. Can these pieces tile a 6×6 square with continuous stripes? We're lucky: the total stripe length is a multiple of 6, & the number of crossings works. One unique tiling exists, up to symmetry. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 12/08/2026

We're having the flooring replaced in the house because my mom is planning on selling it. She reminded me that I picked this linoleum pattern in the laundry room when I was 7. Even then, I liked geometric tilings. #TilingTuesday

Linoleum floor with dryer in the back. There are octagons and rectangles and hexagons and triangles and stuff.

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Alexandre Muñiz @two-star.bsky.social · 04/08/2026

It can be a little hard to see what's going on here. The half-weight-tans are outlined with thick lines. There are overlapping half-weight-tans with different orientations, so it looks like there are smaller tans, but they aren't real. Here are the pieces individually, if that helps:

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Alexandre Muñiz @two-star.bsky.social · 04/08/2026

There are 12 3·½ ◣, (tri-half-weight-tans) if we allow partial half-tan overlaps. They tile a full-weight 3×3 square as shown. Two pairs of pieces have the same shape. A problem where they aren't interchangeable: find another tiling that maximizes the symmetry of the tan diagonals. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 27/05/2026

Since Inflatable Children's Play Structure Discourse seems to be occurring on this hecksite, I wish to note that I still have not received my free inflatable slide rule.

A sign next to a brightly colored inflated structure with the legend, "FREE INFLATABLE SLIDE RULES" followed by some other text that I ignored because it only instructs one on how to use the structure safely, and doesn't tell me how to get my free inflatable slide rule, which is all I care about. There is also a cheerfully light green air pump inflating the structure, and some pedestrians and trees in the background

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Alexandre Muñiz @two-star.bsky.social · 20/05/2026

Turbotoxic was a new word to me, so I had to look it up. Second result:

A not at all dodgy ecommerce site selling Turbotoxic Tea for Weight Loss 6 Bags x 3 Boxes 1 each / dispel turbidity and promote dampness

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Alexandre Muñiz @two-star.bsky.social · 12/05/2026

I hope their bus stop signage lands somewhere in the middle ground between this and Bogotá.

A pole with a sign that says "marta / Bus Stop" with no further information about the bus lines that serve the stop and where they go.

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Alexandre Muñiz @two-star.bsky.social · 06/05/2026

A tiling of 5·½▲, or all of the polyiamonds built from 5 ½-weight cells. I'm using a sort of pinwheel dissection of triangles to show overlapping ½-weight cells belonging to different pieces. The solid triangles represent two overlapping cells belonging to the same piece. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 28/04/2026

I saw this walking in a park in Portland in 2014:

The words "Be Merry!" cut into moss on a short concrete wall, overgrown above with ivy.

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Alexandre Muñiz @two-star.bsky.social · 16/04/2026

Here's one. With additional magic applied:

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Alexandre Muñiz @two-star.bsky.social · 02/02/2026

Happy rectangular February! There are 1522 ways (up to symmetry) to tile a 4×7 rectangle with the 2- through 4-ominoes. Can anything cool be done with these? Maybe, but I haven't thought of anything yet.

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Alexandre Muñiz @two-star.bsky.social · 30/12/2025

New post about variations on adding polyforms sets to make sets of compound polyforms, and notation to use for these. Here's an image from that post of a tiling of a complete set of heterogeneous di-trominoes that admits an interesting coloring. #TililngTuesday puzzlezapper.com/blog/2025/12...

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Alexandre Muñiz @two-star.bsky.social · 25/11/2025

There are 22 ways to connect two half-weight cells to a tromino. To get a proper generalized tiling where all cells have weight 1, the half-weight cells must overlap. Here they are tiling a 11×8 rectangle such that that the overlaps form a single loop. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 17/11/2025

Paul Simon's Rhythm of the Saints came out that year, but Graceland was better. So I got nothing. Wait, hold the presses. Reading, Writing and Arithmetic was a 1990 album and not a 1989 one? That's an easy choice then.

The album cover to Reading, Writing and Arithmetic by The Sundays, with fossil ammonite shells or similar in black and white

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Alexandre Muñiz @two-star.bsky.social · 11/11/2025

There are 20 ways (up to rotation and reflection) to make polyiamonds where each cell edge has one or two notches, and the total number of notches on the perimeter is 7. These have a total of 81 cells, and tile a triangle nicely. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 28/09/2025

But all of those condos weren't the only buildings in the South Waterfront. There was also the non-original location of the original Old Spaghetti Factory restaurant. Oh, and ICE headquarters.

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Alexandre Muñiz @two-star.bsky.social · 11/09/2025

Pentominoes in a 12×12 grid with a sudoku style cell coloring. (All rows, columns and pentominoes contain all five colors.) This pentomino arrangement was discovered by George Sicherman; I found the cell coloring.

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Alexandre Muñiz @two-star.bsky.social · 15/05/2025

Bryce Herdt noted that if you tile a cube with (possibly folded) 4-ominoes, you can get an extra 6th 4-omino at a vertex if you don't allow unfolding that splits an edge apart. That's exactly enough to tile a 2×2 faced cube. I made some with Ankyo blocks. ($1 for a tube of 72 at Target back in '24.)

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Alexandre Muñiz @two-star.bsky.social · 26/04/2025

He might be interesting in polyominoes that tile a torus in ways that require 7 colors. Here's an old graphic of ways to tile a 7×7 torus with heptominoes with χ=7, from www.mathpuzzle.com/4Dec2001.htm

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Alexandre Muñiz @two-star.bsky.social · 16/04/2025

There are 12 tilings of a 3×3 square with an L tromino, two dominoes, and two monominoes, up to symmetry. You can use these squares in a 2×6 rectangular edgematching puzzle. (I've had no luck with 3×4, and suspect it won't work.) #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 09/04/2025

The 2- and 3-ominoes with diagonal stripes passing through the midpoints of cell edges have area 25, and can tile a 5×5 square. It was fun enough to solve manually that I did it again three more times. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 01/04/2025

There are 12 ways to replace two of the cells of an L tetromino with diagonal bars of opposite orientations. They form a unique (up to the symmetries of the square and swapping the bar orientations) 6×6 square tiling with a single cycle of overlapping perpendicular bars. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 18/03/2025

I've been learning how to use @jaapsch.net's PolySolver more effectively lately. I previously tried manually to get symmetrical markings on a tiling with the 12 internal-edge-marked pentiamonds, but had to give up just short. This time I had PolySolver's help. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 11/03/2025

The 16 one-stripe tetrominoes have area 64; we'd like to put them in an 8×8 square. But the stripe length doesn't come out to a multiple of 8, so we can't make it work. Unless we cheat. Here, there are a few positions where stripe continuity is broken to let another stripe pass. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 10/03/2025

New blog post on polyforms with a single stripe: puzzlezapper.com/blog/2025/03...

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Alexandre Muñiz @two-star.bsky.social · 26/02/2025

Applying the same principle to the dominoes and trominoes, there is again one "bad" piece, but the rest have area 49, so we can make a square. Unfortunately, you can't make a loop with an odd number of square cells, so we'll have to settle for a non-circuit path. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 26/02/2025

There are 13 ways to put a bump on one hex of a dihex and a divot on the other. One of them (in red) can't be on a path. The other 12 can make a loop on this figure in exactly one way, up to symmetry/reversal. After I drew this I saw that Alexander Magyarics used the same result in a recent puzzle.

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Alexandre Muñiz @two-star.bsky.social · 26/02/2025

The 16 single stripe tetrominoes don't make anything very elegant by themselves, but if you throw in a pair of unstriped trominoes, you can make a rectangle. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 11/02/2025

Solution. (I labeled it as "graphic" because there wasn't a "spoiler" option.)

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Alexandre Muñiz @two-star.bsky.social · 11/02/2025

A puzzle for #TilingTuesday: These pieces are all of the ways you can put one stripe bisecting opposite hex sides on a trihex. The challenge is to put the pieces in the frame so that the stripes make continuous lines from one edge of the frame to the other.

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Alexandre Muñiz @two-star.bsky.social · 15/01/2025

I was trying to make a tiling of the 2-, 3-, and 4-iamonds with a single directed internal edge on this figure so that the marked edges make a single path. Best I could do was to almost manage it, (excluding one piece,) or to make a tree instead of a path. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 12/12/2024

We still use this beauty here. 44 years young and still going strong.

Whirlpool microwave oven in cabinet from 1981, with amber LEDs, Bookman font with swashes, and an actual Microcomputer. (And a nerd taking a photo with his phone, reflected in the window on the door of the oven

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Alexandre Muñiz @two-star.bsky.social · 27/11/2024

Here's a puzzle you can try on any pentomino tiling: make a crossing-free circuit of king moves passing through every cell of the tiling. The cells within any given pentomino must be visited in an uninterrupted sequence. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 13/11/2024

There are 12 ways to make a pentiamond with a single marked internal cell edge. I tried to tile them with symmetry on the marked edges, but did not have any luck. #TilingTuesday

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Alexandre Muñiz @two-star.bsky.social · 04/11/2024

I have some recreational math followers here now, but they're mainly the same as the ones who follow me on mastodon. I hope crossposting isn't too annoying. New blog post on operations on sets of polyominoes and other polyforms: puzzlezapper.com/blog/2024/11...

A 4-colored symmetrical tiling of the 2+1, 3+1, and 4+1-ominoes.

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Alexandre Muñiz @two-star.bsky.social · 25/10/2024

I have a particularly ridiculous random number generator.

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