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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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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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 ...
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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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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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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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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 ...
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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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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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A constrained, but concerning, celestial confrontation
An entry in Fortnightly Topic Challenge #52: Polyominoes.
This puzzle is a hybrid between Pentominous and Star Battle. Your job is to divide the grid below into pentominoes according to the rules of ...
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Filling a 26x36 grid with trominoes
Let's have 312 L-trominoes of three different colors, 104 trominoes of each color. Can you fill a 26x36 grid with these trominoes without two of the same colors touching side-to-side anywhere? In ...
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Now you're Packing with Portals #2: Hashtag
Place the colored shapes into the white area, without rotations or reflections, so that they fill it perfectly. The gray walls don't just block shapes, though - they act as portals!
When you place a ...
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Now You're Packing with Portals #1
I was staring at my window last night, and daydreaming (nightdreaming?) about filling it with shapes. Suddenly, I was struck with inspiration for a new type of puzzle! Here's a fairly easy instance:
...
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This Sudoku Park iS LIT!
An entry in Fortnightly Topic Challenge #47: "Wacky Sudokus"
The grid below is a normal Sudoku grid with normal Sudoku clues, but the completed grid also houses a Statue Park! The completed ...
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5x5 grid with no tetrominoes containing repeating colors
Paint the cells of a 5x5 grid with 𝑛 colors, such that every possible tetromino found in the grid uses 4 different colors. What is the smallest value of 𝑛 possible in such a coloring?
Here is a ...
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4x4 grid with no trominoes containing repeating colors
Paint the cells of a 4x4 grid with 𝑛 colors, such that every possible tromino found in the grid uses 3 different colors. What is the smallest value of 𝑛 possible in such a coloring?
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a 17X17 grid filled with trominoes of three different colors
Let's have an 17x17 grid. We can fill this grid with 96 trominoes of three different colors, 32 trominoes of each color. On this particular grid the empty single square is the position A1. By visual ...
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Pentomino tiling on wrap-around 5x5 grids
It is known that P pentominoes cannot tile a 5x5 square board.
Q1: If the east and west edges of the 5x5 square board are "wrapping around" (if you move a piece through one of the edges, the ...
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Grids with trominoes
Let's have two 8x8 grids. By visual inspection we see they are filled with trominoes of three different colors. There are 7 trominoes of each color. On the grids the trominoes are not allowed to touch ...
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Forming pairs of trominoes on an 8X8 grid
On an 8x8 grid I put 21 trominoes of thee different colors. Each group of 7 trominoes has one color. By visual inspection we see the trominoes cover the whole surface except the single empty square ...
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Tetrikabe: Hiding in the Corners
This puzzle is dedicated to Sciborg. Copying the dear gentleperson, some of the 4s are hiding in the corners.
Rules: (Nurikabe section shamelessly stolen from an earlier puzzle by @jafe)
Numbered ...
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Elections in the United States of Alfagonia
Elections were held in the 45 electoral districts of the United States of Alfagonia. The Green Party won the election in 23 of the 45 districts. Alfagonia is made up of nine states of five districts, ...
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Hetero-F(our|ive)-Cells
This is a hybrid of Four Cells and Five Cells (uses pentominoes instead of tetrominoes), with a global no-repeated-piece rule.
Rules:
The grid is to be divided along the grid lines into areas ...
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Tetrikabe: Socially Distanced Fours
Pentomino Nurikabe is still elusive, but here is another Tetromino Nurikabe! I'm not sure if the 4s are actually socially distanced enough. (The ones on the right and bottom are doing better than the ...
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Tetromino Nurikabe: Five Fours
I enjoy combining polyominos with grid-deductions. My current plan is to create a Pentomino Nurikabe. But that sounds hard, so I made this Tetromino Nurikabe as practice first. I think it came out ...
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Wait, so how many mines are there? A tetromino minesweeper
Here's another tetromino minesweeper. I have bolded where the rules differ between this one and my first tetromino minesweeper
Rules:
A number indicates how many adjacent (including diagonally ...
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Tetromino minesweeper: the Amphitheater
This is a minesweeper puzzle with a tetromino twist. The goal is to place mines in the grid, following a few constraints.
Rules:
A number indicates how many adjacent (including diagonally adjacent) ...
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L-tromino pair!
Amy is playing with different polyominoes. She suddenly thinks of a problem as follows.
Choose two positive integers $m,n$. If we can use only L-trominos to tessellate a $m\times n$ rectangle with no ...
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Hand tiling - 4x inflated pentominoes with pentominoes and tetrominos
This is a manual tiling puzzle. Difficulty level always hard to estimate, but I would say a few minutes per solution for an accomplished solver, all the way to just about impossible for someone like ...
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Square made up with polyominoes
A 3 x 6 rectangle has 2 holes in it as shown. Can you cut it into 3 polyominoes with different areas so that they can form a square? The pieces can’t be flipped when they form the square and two ...
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A Rook's Territory in the Chessboard
Shade 32 cells, four on each row and column, of an 8 x 8 blank chessboard (all its cells originally white) so that a rook sitting on any shaded cell can reach any other shaded cell, moving just along ...
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Largest set of independent hexominoes
What is the largest set of hexominoes that can be found in which no two of them are such that one can be converted into the other by cutting out one of its component squares (thus obtaining a ...
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Let's Play Tetris!
Fill the whole grid with Tetrominos.
Every cell must be part of exactly one Tetromino.
Tetrominos can be rotated as necessary.
The colored clue cells must be part of the indicated type of ...
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Finding the most flexible of all 35 hexominoes
Of all 35 hexominoes, which is (or are) the most flexible of all, that is, the one (or ones) that can be converted into the most other hexominoes just by cutting out one of its component squares (thus ...
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Generating all hexominoes by cutting and pasting
Place the 35 hexominoes around a circle in such a way that if two of the hexominoes find themselves next to each other, it is because one of the two can be obtained from the other by cutting out one ...
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Polyominoes to construct alphabet
It is possible, using a set of just 10 polyominoes, to construct any one of the 26 letters below. Can you find such a set?
When constructing, polyominoes may be rotated and flipped, but may not ...
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