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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3 votes
3 answers
483 views

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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7 votes
1 answer
178 views

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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9 votes
3 answers
961 views

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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9 votes
3 answers
1k views

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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10 votes
1 answer
757 views

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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  • 289
3 votes
1 answer
310 views

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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14 votes
3 answers
2k views

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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  • 141
2 votes
1 answer
184 views

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 votes
2 answers
138 views

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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2 votes
1 answer
187 views

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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6 votes
2 answers
256 views

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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  • 163
9 votes
2 answers
482 views

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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  • 10.6k
11 votes
1 answer
225 views

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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18 votes
4 answers
1k views

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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  • 98k
14 votes
4 answers
1k views

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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  • 1,283
-1 votes
2 answers
192 views

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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6 votes
2 answers
244 views

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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2 votes
1 answer
91 views

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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2 votes
1 answer
241 views

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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1 vote
3 answers
235 views

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 vote
1 answer
89 views

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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23 votes
1 answer
810 views

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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  • 98k
18 votes
1 answer
477 views

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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-2 votes
1 answer
126 views

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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14 votes
2 answers
656 views

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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  • 1,570
42 votes
2 answers
2k views

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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  • 1,570
15 votes
1 answer
540 views

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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1 vote
3 answers
134 views

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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3 votes
3 answers
412 views

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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-3 votes
1 answer
154 views

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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7 votes
2 answers
378 views

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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4 votes
1 answer
283 views

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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2 votes
1 answer
316 views

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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9 votes
3 answers
492 views

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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  • 9,174
-5 votes
1 answer
191 views

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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13 votes
1 answer
454 views

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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  • 10.6k
13 votes
1 answer
496 views

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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  • 9,174
11 votes
1 answer
382 views

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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  • 9,174
14 votes
2 answers
1k views

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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  • 9,174
13 votes
2 answers
700 views

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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  • 9,174
8 votes
1 answer
169 views

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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  • 5,520
7 votes
0 answers
126 views

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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9 votes
2 answers
272 views

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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16 votes
2 answers
2k views

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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7 votes
1 answer
247 views

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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13 votes
2 answers
342 views

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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  • 683
7 votes
2 answers
390 views

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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11 votes
1 answer
395 views

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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16 votes
2 answers
809 views

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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  • 8,760