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Lana, 13 days ago to random

Anyone arguing in favor of arming school teachers needs to first explain to me where in the budget you're going to find the money to buy 27 Glocks when you cheapskates won't even buy us printer toner.

two_star, 15 days ago to random

Back in my blog's first year, I asked if it was possible to make a certain tiling of a pair of tetromino sets with a monomino hole such that the edges of the polyominoes could be tiled by the 16 tetrasticks. At #G4G15, William Waite gave me a puzzle using both polyominoes and polyedges that he said was inspired by a conversation we'd had about the possibility of a combined polyedge/polyomino tiling puzzle. (That puzzle uses a simpler and easier to tile set of pieces.)

Lately, I've been realizing that Jaap Scherphuis' PolySolver is capable of solving a lot of problems I didn't have another way to solve, so I tried it on this one. It turns out that there is a unique solution! (Unfortunately, no solution with the monomino in the center, as I'd hoped.)

#TilingTuesday

two_star, 1 month ago to random

New blog post on polyforms with edge markings that trace the border of a tiling. https://puzzlezapper.com/blog/2024/04/border-marking/

Part of this is the pizza problem I posted about previously, but I thought the crusty pizza metaphor was a little too cheesy. The polyiamond result is new though.

#TilingTuesday

two_star, 1 month ago to random

Here's a puzzle game. I call it Reverse the List of Integers. How it works is, you start with a list of positive integers, (e.g. [7, 5, 3]) and your goal is to make the same list, in reverse ([3, 5, 7]). You have two moves you can make:

1. Split an integer into two smaller integers. (e.g. [7, 5, 3] → [6, 1, 5, 3])
2. Combine (add) two integers into a larger one. (e.g. reverse the last e.g.)

There are two restrictions that seem natural for making this into an interesting game:

1. You can never make an integer greater than the largest integer in the original list.
2. You can never make a move that results in the same integer appearing in the list more than once.

With these rules, even pretty simple lists can make non-trivial puzzles. (Try it with [7, 5, 3].) Some questions:

1. What are good algorithms, or even general strategies, for solving these?
2. For a given n, there must be some puzzle where n is the largest number in the list, and the number of moves required to solve the puzzle is maximized. What does the sequence of maximal required moves look like as a function of n? What do the "hardest" puzzles look like? Is there a way to determine either without using brute force?

mishellbaker, 1 month ago to random

Imagine being a Neolithic farmer, out tending your little crops by hand under a bright blue sky, and then suddenly... the sun disappears, and the world goes dark. Imagine your horror - hearing the cries and sobs of the people in your village as they run outside, bewildered and terrified as day turns to night, against all they understand of the world.

Imagine the flood of relief when light returns. Imagine arms raised toward the sky in gratitude, never taking sunlight for granted again.

two_star, 1 month ago to random

New blog post, on what happens when edgematching tiles break out of their rectangular cages... and go into slightly larger rectangular cages: https://puzzlezapper.com/blog/2024/04/edgematching-to-the-stars/

These tiles are equivalent to MacMahon's 24 tiles with 3 edge colors. (Tiles may be rotated, but not flipped.) The challenge here is to place the tiles on an 8×8 board so that the semicircles connect on adjacent squares, the triangles see another triangle over a distance of at least one square, and the x's see nothing but empty space to the edge of the board.

#TilingTuesday

two_star, 1 month ago to random

The tetrakis grid tetratans and pentatans can tile a square. I'm sure somebody else has to have done this tiling before.

#TilingTuesday

two_star, 2 months ago to random

If you put two arrows at headings of distinct multiples of τ/8 at the center of one of the cells of a double-sided 2×2 square tile, you get 16 different tiles. You can put those tiles in a 4×4 grid, and make paths connecting the arrows. Reasonable rules seem to be:

1. All arrows are connected into a single path.
2. The path may not enter any cell with arrows in any direction that does not correspond to an arrow.

Closed circuits should be possible, and one might want to set additional challenges like minimizing or maximizing the path length or the number of crossings. But honestly, just finding any path at all was a pretty difficult manual puzzle for me, so I'm not sure it needs extra challenge.

#TilingTuesday

18+ two_star, 2 months ago to random

A customer of a pizza parlor promises to put in a large recurring order that will ensure its financial stability, but only if it can meet their very particular demands:

The pizza must be rectangular with a crust around its perimeter, and each piece must be shaped like a domino or tromino (either L shaped, or 1×3 rectangle.) Each piece must be distinct from all of the others when crust presence and position is considered. (Reflections and rotations of a piece are considered identical.) Furthermore, every combination of piece shape and crust that can exist on the pizza must occur exactly once. ("Can exist" is doing a little bit of work. Some crust positions can't exist. Which ones might depend on the pizza's dimensions!)

Remarkably, an acceptable order for this customer is possible. Hence, I offer a puzzle in two parts: first, find a valid set of pizza pieces, and then, find a tiling of a pizza with them.

(Nah, I don't expect anyone to stop scrolling to solve a puzzle. But since I live in hope, I'm marking the images as spoilers. This one is just the pieces.)
(1/2)

#TilingTuesday

two_star, 3 months ago to random

A recombination move on an n-omino tiling joins a pair of adjacent n-ominoes and then breaks them apart into a different pair. A locked tiling is one where no recombination moves are possible.

Shown are the smallest square locked tilings for 4-ominoes and 5-ominoes. Remarkably, in both cases, there is a unique smallest tiling. These results and others are discussed in Jamie Tucker-Foltz's paper, Locked Polyomino Tilings: https://arxiv.org/abs/2307.15996

#TilingTuesday

two_star, 3 months ago to random

Here's a variation on polytans. Start with a unit tan as usual, but in addition to joining another unit tan to it, you can join the leg of a larger tan to the hypotenuse of a previous tan. There are 14 subtiled tri-inflatable-tans, and the set can tile a 5×6 rectangle. I played with it manually, and it feels like a good manual puzzle. For a bit of extra challenge, I looked for a solution where all of the interior long edges between pieces (length 2 or 2√2) join edge to edge, and one where none of them do. These are below.

#TilingTuesday

two_star, 3 months ago to random

There are 18 diditans, if those containing different orientations of the component tans are considered distinct. They can tile a 6×6 square, as shown.

#TilingTuesday

two_star, 4 months ago to random

Here's the blog post on extremal polyominoes I was threatening: https://puzzlezapper.com/blog/2024/01/extremal-structure-excluding-polyforms/

Much thanks to @domotorp and Renan Gross for tracking down the key result the post needed. The graphic below is a 142-omino with no 4 equally spaced cells on the same line, proved maximal by Jan Kristian Haugland.

#TilingTuesday

two_star, 5 months ago to random

I've been meaning to write a blog post about extremal polyforms. The largest polyomino with no 3 cells equally spaced on the same line has 4 cells. The largest polyomino with no 4 cells equally spaced on the same line has 142 cells, as proved by Jan Kristian Haugland. (See https://arxiv.org/abs/2004.12801 )

I'm maybe 80% sure I've seen the no 5 cells equally spaced problem somewhere, but I can't find it again. I had in my notes that the largest polyking with no 3 cells equally spaced was conjectured to be 48 by members of a bulletin board called Zompist, but the post is gone and the Wayback Machine doesn't have it. So I set myself the puzzle of recreating it, and did so tonight.

#TilingTuesday

two_star, 5 months ago to random

Just under the wire for #TilingTuesday, a failed attempt at a meta 3-coloring of the 3+2-ominoes. A meta-3-coloring would involve a 3-coloring of the component dominoes and trominoes, and a 3-coloring of the pentominoes they form together, where the color of the pentomino is the color that is missing from its components.

two_star, 5 months ago to random

I got mentioned on this Numberphile video that just came out. The funny bit is that they used a photo of me that was taken 18 years ago when I was interviewed for Jason Scott's documentary on text adventures, Get Lamp. Okay, the funny bit about the funny bit is that Scott barely used the footage from the interview. It's not in the main feature at all; there's just a tiny snippet in a DVD extra. https://www.youtube.com/watch?v=3akBMSJ37Uk
The mention of me is at the 9:15 mark.

fractalkitty, 6 months ago to RPG

This was my little hobby project for the day. If you are short on writing prompts - pick a portal.

https://porthales.art/

#salemOregon #funWithData #porthales #RPG #dataArt #mathArt #python #creativeCoding #NaNoWriMo

mishellbaker, 6 months ago to random

Why am I learning nerdy computer stuff at my age after a lifetime of being a clueless user?

I'm just tired of feeling helpless when stuff goes wrong with tech that I use all day every day. There are things in life I can't control no matter how much I learn. Computers, on the other hand, don't need to be a mystery.

johncarlosbaez, 10 months ago (edited 10 months ago) to random

Yeah, cosmic gravitational noise is cool... but check out this brand-new image of the Milky Way taken in neutrinos!

https://drexel.edu/news/archive/2023/June/Drexel-Physicists-Produce-New-Images-of-Milky-Way-Galaxy

Thanks to @bstacey for pointing this out.

The neutrinos are in blue, while the dust clouds and other stuff were photographed in visible light and superimposed just for context. Here's an animated gif that fades the neutrino view in and out:

https://drexel.edu/news/~/media/Drexel/Core-Site-Group/News/Images/v2/story-images/2023/June/Neutrino-Animated-Gif_1920x1080_wide_IG_Fin.ashx

ColinTheMathmo, 11 months ago to random

Maths teachers asked: Do you think you are a mathematician?

https://tommaths.blogspot.com/2023/06/do-maths-teachers-think-theyre.html

christianp, 11 months ago to random

I have an M&S gift card and I'm struggling to spend it. Their "long" trousers are 3 inches shorter than my legs. I'm tall, but I walked past three people at least as tall as me on the way to the shop.
And if your feet aren't between size 9 and size 12, Mr Marks and Mr Spencer aren't interested in selling you socks