Alexandre Muñiz
@two-star.bsky.social
Math puzzles, choral singing, Irish and Morris dancing, SF, fantasy, and romance reading, shiny object collecting.
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.
November 17, 2025 at 8:56 AM
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.
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
November 11, 2025 at 5:36 PM
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
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.
Oh, and ICE headquarters.
September 28, 2025 at 3:24 AM
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.
Oh, and ICE headquarters.
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.
September 10, 2025 at 11:20 PM
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.
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.)
May 15, 2025 at 6:12 PM
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.)
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
April 26, 2025 at 1:24 AM
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
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
#TilingTuesday
April 16, 2025 at 6:43 AM
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
#TilingTuesday
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
April 9, 2025 at 6:09 AM
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
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
April 1, 2025 at 7:13 PM
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
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
March 18, 2025 at 11:14 PM
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
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
#TilingTuesday
March 11, 2025 at 2:05 PM
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
#TilingTuesday
New blog post on polyforms with a single stripe: puzzlezapper.com/blog/2025/03...
March 10, 2025 at 3:16 PM
New blog post on polyforms with a single stripe: puzzlezapper.com/blog/2025/03...
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
February 26, 2025 at 12:01 AM
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
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.
February 26, 2025 at 12:01 AM
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.
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
February 26, 2025 at 12:00 AM
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
Solution. (I labeled it as "graphic" because there wasn't a "spoiler" option.)
February 11, 2025 at 6:58 PM
Solution. (I labeled it as "graphic" because there wasn't a "spoiler" option.)
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.
February 11, 2025 at 6:58 PM
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.
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
January 15, 2025 at 7:59 AM
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
We still use this beauty here. 44 years young and still going strong.
December 12, 2024 at 10:47 PM
We still use this beauty here. 44 years young and still going strong.
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
November 27, 2024 at 6:26 AM
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
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
#TilingTuesday
November 13, 2024 at 7:21 AM
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
#TilingTuesday
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...
New blog post on operations on sets of polyominoes and other polyforms: puzzlezapper.com/blog/2024/11...
November 4, 2024 at 2:34 AM
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...
New blog post on operations on sets of polyominoes and other polyforms: puzzlezapper.com/blog/2024/11...
I have a particularly ridiculous random number generator.
October 25, 2024 at 4:55 PM
I have a particularly ridiculous random number generator.
Extremely disappointing sign.
July 21, 2024 at 8:25 AM
Extremely disappointing sign.