68 votes
Accepted

Can you put L trominos to fill the figure?

Answer: Reasoning:
Magma's user avatar
  • 5,259
52 votes
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 ...
Victor Stafusa - BozoNaCadeia's user avatar
45 votes
Accepted

`print("Hello, World!")`

... ... ... ... ... ... ... ...
loopy walt's user avatar
  • 21.4k
39 votes

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 ...
BlueHairedMeerkat's user avatar
26 votes
Accepted

Which heptomino is it obvious can't tile the plane?

The one that
RobPratt's user avatar
  • 13.7k
25 votes
Accepted

Now You're Packing with Portals #1

This works! (I think) (Hopefully that’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 ...
Beastly Gerbil's user avatar
23 votes

Tiling with T-tetrominos in gravity

I think that this tiling is a valid Tetris stack:
M Oehm's user avatar
  • 60.8k
23 votes
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 ...
Daniel Mathias's user avatar
22 votes

A Rook's Territory in the Chessboard

Here's an expandable solution for $n\ge 5$ (even or odd):
RobPratt's user avatar
  • 13.7k
21 votes
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.)
Deusovi's user avatar
  • 146k
21 votes

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 ...
Jaap Scherphuis's user avatar
21 votes
Accepted

Polly O'Mino's Hexcellent Adventure

COMPLETED GRID The first step: Next: An important side note: Moving on: The top shaded region: Hopefully, finishing up:
Jeremy Dover's user avatar
  • 27.8k
21 votes

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 ...
xd y's user avatar
  • 525
21 votes
Accepted

Most polyominoes in an 8x8 grid

user1502040's user avatar
20 votes
Accepted

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 ...
Steve's user avatar
  • 3,875
20 votes

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.
ApexPolenta's user avatar
  • 2,690
20 votes
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:
Carmeister's user avatar
  • 2,205
19 votes

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 ...
user21820's user avatar
  • 1,137
19 votes
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 ...
loopy walt's user avatar
  • 21.4k
19 votes
Accepted

Gimme five (Pentomino puzzle)

First, focus on Now, move on to
Bubbler's user avatar
  • 14.1k
18 votes

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 &...
RobPratt's user avatar
  • 13.7k
17 votes
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:
Dave's user avatar
  • 186
17 votes

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
A. Rex's user avatar
  • 955
17 votes

Smallest rectangle to put the 24 ABCD words combination

Pretty sure that the following is minimal.
Ed Pegg's user avatar
  • 271
16 votes

Polyominoes to construct alphabet

Using:
JMP's user avatar
  • 35.6k
16 votes

Tiling with Js and Ls

UPDATE Down to 6 outcolour tiles Here is one way:
loopy walt's user avatar
  • 21.4k
15 votes
Accepted

Pentominoes On the Edge

I found these solutions while playing around on https://www.scholastic.com/blueballiett/games/pentominoes_game.htm.
wildBillMunson's user avatar
15 votes

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, ...
Bass's user avatar
  • 77.4k
15 votes
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:
Amoz's user avatar
  • 27k
14 votes

What is the minimum-sized Blokus board which can contain all pieces?

Wow, that sure is tight. And yes, even though it doesn't look like it at the first glance, the I and T pentominoes are legally connected to each other :-) This took surprisingly long to find and (...
Bass's user avatar
  • 77.4k

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