# Tag Info

Accepted

• 5,259
Accepted

### Tiling with T-tetrominos in gravity

TLDR: I'll fill the board and prove that the solution is unique. First, let's start by: I'll paint those green: Let's repeat those steps a few more times, using orange, blue, red and purple, in ...
Accepted

### print("Hello, World!")

... ... ... ... ... ... ... ...
• 21.4k

### Hexominos from pentominos, heptominos from hexominos

Let us start by considering this hexomino: It is clear that there is only one pentomino that can be extended to this: And since we have to use that pentomino, we can tick off several hexominoes that ...
• 2,046
Accepted

The one that
• 13.7k
Accepted

### Now You're Packing with Portals #1

This works! (I think) (Hopefully thatâ€™s clear enough how the shapes go) I got this mostly by thinking about how the blue and red can be placed such that the top and bottom of the green can be ...
• 58.4k

### Tiling with T-tetrominos in gravity

I think that this tiling is a valid Tetris stack:
• 60.8k
Accepted

### A Rook's Territory in the Chessboard

I started with this: Pushed things this way and that, ended up with this: Similarly, on 9x9: And on 10x10: It took me a while to get there, but that one suggests an emerging pattern. And here is ...
• 14.9k

### A Rook's Territory in the Chessboard

Here's an expandable solution for $n\ge 5$ (even or odd):
• 13.7k
Accepted

### Near-fill with 3x1 long triominos, how to do a different void square than the center square?

The trick to this puzzle is to: (And here are those tilings: the center was already given, and the rest are obtainable from these by rotation.)
• 146k

### Covering an 8x8 grid with X pentominoes

The X-pentomino tiles the plane, so that tiling is a good way to start. There are two ways to cut an 8x8 region out of that tiling. If one of the 4 central squares of the 8x8 region has an X centred ...
• 53.3k
Accepted

COMPLETED GRID The first step: Next: An important side note: Moving on: The top shaded region: Hopefully, finishing up:
• 27.8k

### How many distinct pentominoes are possible to place on an 8 x 8 board?

With integer programming, I managed to place like this. Here is my formulation. I happened to solve a similar model to solve a puzzle called One puzzle a day. Let $B$ be the set of cells in the 8x8 ...
• 525
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• 857
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### Filling the plane with two colors

FINITE PORTION OF ANSWER This can be extended infinitely in all directions - see my route to solving below for how. First a detour to explain how I made a tool (which competing answers could also ...
• 3,875

### How to fully tile an 8 by 8 square with Z-tetrominoes?

If reflections are not allowed: The figures below show why. If reflections are allowed: See figure below showing the top three rows of the 8x8 square.
• 2,690
Accepted

### Tiling a 5-by-5 bathroom with L-shaped triomino tiles

The missing square has to be one of these: Demonstration that any of these is possible:
• 2,205

### How many distinct pentominoes are possible to place on an 8 x 8 board?

I solved this completely by hand. Here is a clean proof of its optimality. No computer is needed. Mere pencil and paper suffice. Expand each pentomino by adding little right-angled isosceles ...
• 1,137
Accepted

### Packing pentominoes in a circle

UPDATE 2 A minor improvement. New best radius Arrangement /UPDATE 2 UPDATE New best radius: using arrangement /UPDATE I get a radius of about using the following scheme which is obviously ...
• 21.4k
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### Gimme five (Pentomino puzzle)

First, focus on Now, move on to
• 14.1k

### How to fully tile an 8 by 8 square with Z-tetrominoes?

\begin{matrix} 9 &1 &9 &5 &5 &9 &1 &9 \\ 1 &-11 &-3 &-7 &-7 &-3 &-11 &1 \\ 9 &-3 &5 &1 &1 &5 &-3 &9 \\ 5 &-7 &...
• 13.7k
Accepted

### Polyominoes to construct alphabet

I haven't tried one of these before; I just stumbled across the question by accident. But I think I have an answer. You can build all 26 letters if you have a set containing: Image below:
• 186

### The universal ticket

The previously best-known solution has score of 165, with the following grid: From a clever brute-force search, one can learn that However, you can do better! The ticket achieves a score of
• 955

### Smallest rectangle to put the 24 ABCD words combination

Pretty sure that the following is minimal.
• 271

Using:
• 35.6k

### Tiling with Js and Ls

UPDATE Down to 6 outcolour tiles Here is one way:
• 21.4k
Accepted

### Pentominoes On the Edge

I found these solutions while playing around on https://www.scholastic.com/blueballiett/games/pentominoes_game.htm.
• 2,511

### The universal ticket

Very unlikely to be optimal, but got to 120 on my first go: Approach: mess around with the problem until it becomes clear that connectivity of the squares will be the main problem. invent glue, ...
• 77.4k
Accepted

### The woefully underclued crossword

Answers to clues: At this point, given the tag, it looks like we are looking for So let's start filling the grid: Completed grid:
• 27k