Questions tagged [polyomino]
A geometric puzzle centered around geometric figures formed from unit-squares, or a puzzle that uses polyominoes as an integral part.
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Minimum lines needed to draw the 12 pentominoes
You need 4 lines to draw the monomino and the same for the domino
You can draw the 2 trominoes with 7 lines
For the five tetrominoes I could do it first with 16 lines
Then 15 lines
And my best try ...
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Fewest polyominoes adjacent to 3 copies
What is the smallest positive number of polyominoes P, such that
You can place grid aligned copies of P without any overlap; and
Each polyomino is adjacent to exactly 3 other polyominoes.
...
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Smallest polyomino adjacent to 3 copies
What is the smallest polyomino P in number of cells, such that
You can place grid aligned copies of P without any overlap; and
Each polyomino is adjacent to exactly 3 other polyominoes.
Polyominoes ...
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The Nine Gardens Of Eden
This puzzle is part of the Monthly Topic Challenge #11: Now in 3D.
There are nine distinct known three-cell Garden of Eden patterns in the Life Without Death cellular automata, including the two well-...
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Tetromino Jigsaw Madness
This is part 23 of the puzzle series Around the World in Many Days. Each part is solvable on its own.
Dear Puzzling,
This puzzle is a crossword-jigsaw hybrid. Cover the white area of the grid with ...
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13
votes
1
answer
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Sardines and Octopi
This is part 21 of the puzzle series Around the World in Many Days. Each part is solvable on its own.
Dear Puzzling,
The thick black lines in this grid form a LITS puzzle. Shade an orthogonally ...
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8
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4
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Smallest rectangle to put the 24 ABCD words combination
Put in the smallest possible size board all combination of 4 quantity of letters. Crossword must be connected. And can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters
Example for:...
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Most polyominoes in an 8x8 grid
What is the most number of distinct free polyominoes you can form by painting an 8x8 grid in two colours? Here a polyomino is a set of orthogonally adjacent cells of the same colour, so polyominoes of ...
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How to fully tile an 8 by 8 square with Z-tetrominoes?
Is it possible to fully tile an 8 by 8 square grid using only Z-tetrominoes? (I don't know the answer...)
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Coasting Along the Coast
This is part 14 of the puzzle series Around the World in Many Days. Each part is solvable on its own.
Deаr Puzzling,
The larger grid is a Fillomino puzzle. Each of the six different letters in the ...
- 75.6k
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Set of magic polyominoes that can tile a square
Let's first look at this square grid of numbers.
The 9 squares in yellow is what we are looking at and the green numbers are the sums for the digits within the rows and columns. The red squares are ...
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Polyominos packing into a square
Rules of the game:
Take a square grid nxn.
Populate the grid with polyonimoes of area size 1 to area of 9.
Polyominoes can be any shape.
There must be one each of every size polyomino in every row ...
- 601
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votes
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"Symmetric" Tetrikabe
This puzzle's theme is inspired by one from Grandmaster Puzzles' "The Art of Puzzles", but the puzzle itself is original.
Rules: (Nurikabe section shamelessly stolen from an earlier puzzle ...
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From Before Caesar
This is part 4 of the puzzle series Around the World in Many Days. Each part is solvable on its own.
Deаr Puzzling,
How have you been? I hope you don’t mind me showing up a little early this time ...
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The woefully underclued crossword
This puzzle is part of the Monthly Topic Challenge #4: Cross-*non*-words
Giving clues for everything makes things way too simple. In this crossword, four clues are not given and you must find a way ...
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Cover a 15×8 board with the pentominoes [closed]
Cover the entire area of the 15×8 square shape with two complete sets of 12 different types of pentominoes.
The pentominos can be rotated and flipped.
Two pentominoes of the same type must not be ...
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What approach can I use to solve this wooden packing puzzle?
I am looking for an approach to solve a wooden packing puzzle which my three-year-old got as a present.
We enthusiastically unpacked and disassembled the puzzle when she got it. (It came put-together ...
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Solving a 5x5 pentomino with only certain shapes
I have a physical Pentomino puzzle lying around, which contains 2 F pieces, one Y piece, one T piece and one W piece. The area into which the squares are supposed to fit in is just a little under 6 ...
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Shaka/shawaka: Trominoes
This is a shaka/shawaka puzzle. Place black triangles in some white cells in the grid – formed by dividing a cell diagonally and painting one side black – so that each remaining white area forms the ...
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Shaka/shawaka: An introduction
This is a shaka/shawaka puzzle. Place black triangles in some white cells in the grid – formed by dividing a cell diagonally and painting one side black – so that each remaining white area forms the ...
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Pentomino - is there any solution with the straight-bar piece in the middle of a rectangle?
Is there a solution for a straight-bar piece not touching the edge of the rectangle? By rectangle solution, I mean either one of the patterns 15x4, 12x5, or 10x6. By straight-bar piece, I mean the ...
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Packing pentominoes in a circle
You want to prepare a pizza of 12 flavors. You have 12 oddly-shaped pieces of cheese that you decide to use for the pizza. The shapes happen to be ...
Oh, well, forget it! This isn't going to be ...
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15 x 15 polyomino
You cannot move the red squares
You cannot rotate the blocks
You cannot have 2 block of the same color touching each other, not even diagonally (by their corners)
Grey blocks cannot touch a red square,...
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Block fill in date puzzle
I have been trying this puzzle for HOURS!!! The goal is the fit all the pieces but not cover Aug or 1. You can rotate the pieces.
Credit to www.dragonfjord.com
The link shown at the bottom of the ...
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votes
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answer
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Tiling with dominoes then with tetrominoes
For reference, here are the five tetrominoes:
Suppose you join ten dominoes to make a polyomino made of twenty unit squares. Is it possible that you can tile the polyomino using all the five given ...
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Tiling a 5x5 square with five pentominoes AND a Latin square
Suppose that a 5x5 square has been tiled with five (not necessarily distinct) pentominoes. Is it true that there will necessarily exist at least one Latin square of size 5x5 (using the numbers 1,2,3,...
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The universal ticket
I am submitting a very interesting problem from a French mathematical recreation site:
http://www.diophante.fr/problemes-par-themes/g-probabilites/g2-combinatoire-denombrements/1434-g248-le-billet-...
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Polyominoes inside a 10x10 grid
Can you place five dominoes, five trominoes, five tetrominoes, five pentominoes and five hexominoes inside a 10x10 grid, such that:
No two polyominoes overlap
No two polyominoes of the same size (by ...
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3
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Multi-colored polyominoes inside a 7x7 grid
Can you place four red trominoes, four green tetrominoes and four blue pentominoes inside an 7x7 grid, such that:
No two polyominoes overlap
No two polyominoes of the same color touch each other ...
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Tetromino in a Pentomino Lair
Inspired by this question:
Can you fit twelve pentominoes (not necessarily distinct) and one tetromino inside a 10 x 10 grid such that they do not overlap or touch each other orthogonally (...
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Fitting pentominoes inside a 10x10 grid
What is the most number of pentominoes that you can fit inside a 10x10 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically)?
Bonus: what is the most number ...
- 31.8k
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Ten tetrominoes inside an 8x8 grid
Can you place ten tetrominoes inside an 8x8 grid, such that they do not overlap or touch each other orthogonally (horizontally or vertically) ?
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How to solve this Pentomino puzzle?
The following Pentomino board has exactly one solution:
The solution is known:
I'm trying to solve this board manually, but it is so difficult that I came to believe it is impossible.
I noticed ...
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How many distinct pentominos can be placed on a 8×9 board?
Upon proving optimality of an 8-pentomino solution for an 8×8 board, I was curious to see whether there is a 9-pentomino solution for an 8×9 board, namely a way to arrange 9 distinct pentominos within ...
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How many distinct pentominoes are possible to place on an 8 x 8 board?
Rules
Place some pentominoes into an 8 x 8 grid. They do not touch each other. They can touch only diagonally (with corner).
Pentominoes cannot repeat in the grid. Rotations and reflections of a ...
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Sets of tetrominoes forming a magic square
Is it possible to place $n$ sets of five free tetrominoes on a $K \times K$ square grid, such that:
No two tetrominoes overlap.
Tetrominoes can be rotated or flipped.
Every row, column and two main ...
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2
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L tetrominoes forming an 8x8 magic square
This is a puzzle from Rodolfo Kurchan.
Can you place 10 L-shaped tetrominoes on a 8x8 grid, such that:
No two tetrominoes overlap.
Tetrominoes can be rotated and flipped.
Every row and column ...
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votes
1
answer
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Progressive Daedalian Opus
The 1990 Game Boy game Daedalian Opus is essentially a series of 36 pentomino puzzles. In the first level, however, you only have three pentominos; the rest are introduced in the levels after that, ...
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2
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Jigsaw puzzle: packing pentominoes into a rectangle
I've got this jigsaw puzzle that I can't figure out. The major problem is that there are no signposts on whether a piece is in the right place. How does one get all the pieces into the 6x10 container? ...
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Christmas tree LITSO
Inspired by PSE Advent Calendar 2021 (Day 13): A Christmas Hokuro, I challenged myself to create a Christmas tree-shaped puzzle. Unfortunately I had to edit the shape a little bit because... reasons. ...
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Tiling three pears with three-pair hexominos
The 21 hexominos below are all those that can be made by joining three dominos together (i.e. they have a perfect matching with respect to the graph of their squares) and are not rectangles. The ...
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It's a LITS! And a... um...?
I've combined two of my favourite puzzle types - a LITS grid-deduction puzzle and a, er... a, um... you know, I could have sworn I wrote it down here somewhere!
Click on the image for a resolution ...
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Tiling with Js and Ls
In this puzzle you must tile the plane with identically sized colored L and J tetraminos. To start I will place two of them like so:
Your task will be to tile the entire rest of the plane meeting ...
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Rectangles and squares of trominoes filling a grid
Let's have a board 24 squares by 24 squares. This board is to be filled with trominoes of three different colors. There are equal numbers of trominoes of each color. The board is to be filled with ...
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Most polyominoes on a Rubik's cube
What is the most number of distinct free polyominoes you can form on the faces of a standard 3x3x3 Rubik's cube? Here a polyomino is considered as a set of orthogonally-adjacent cells of the same ...
- 31.8k
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1
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Polyominoes on a Rubik's cube
Is it possible to obtain a tetromino and a pentomino of different colour on each face of a standard 3x3x3 Rubik's cube?
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A solitaire Blokus problem on a rectangular board
Rules
As in Blokus, you have a total of 21 pieces (every piece from monomino to pentomino) in hand:
All of these polyominoes are free, this means that you can rotate or flip them as you wish before ...
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Test of Pentominoes
These are pentominoes, with letter codes:
Create 4 yes/no questions which uniquely classify each pentomino.
Examples of such questions are:
Does it have rotational symmetry?
Does it have reflection ...
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1
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Polyominoes piece puzzle, image was a storefront
When I was growing up, my family had a jigsaw puzzle of several store fronts, where you could see different people running, buying, and some kids. All the stores had letters and art. The pieces where ...
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Polly O'Mino's Hexcellent Adventure
An entry in Fortnightly Topic Challenge #52: Polyominoes.
I had heard that my good friend Ingrid Deduction was back in town, so I popped round to her apartment today, only to find she'd got herself a ...
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