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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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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1answer
74 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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1answer
732 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 ...
18
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1answer
379 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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1answer
101 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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2answers
606 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 ...
42
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2answers
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: ...
15
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1answer
453 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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3answers
91 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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3answers
357 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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1answer
136 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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2answers
339 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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1answer
265 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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1answer
308 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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3answers
440 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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1answer
181 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, ...
13
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1answer
426 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 ...
12
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1answer
443 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 ...
11
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1answer
334 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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2answers
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 ...
13
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2answers
656 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) ...
8
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1answer
154 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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0answers
109 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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2answers
262 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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2answers
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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1answer
231 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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2answers
298 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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2answers
361 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 ...
11
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1answer
386 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 ...
16
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2answers
789 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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2answers
179 views

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

Rules: Each player has the twelve pentominoes, five tetrominoes, two trominoes, one domino, and lone square. These may be flipped and rotated in any manner. The board on which these are to be placed ...
12
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3answers
390 views

Fewest polyominoes to construct digits

What is the fewest polyominoes you need so that any one of the numbers $0$ to $9$ can be constructed? When constructing, polyominoes may be rotated and flipped, but may not overlap. Bonus: How few ...
20
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3answers
654 views

Filling the plane with two colors

In this puzzle you must tile the plane with colored T-tetraminos. I will start by laying down 3 of them for you like so: Your task will be to tile the entire rest of the plane meeting the following ...
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2answers
331 views

Hand tiling puzzle demonstrating Eisenstein triple $c^2 = a^2 -ab + b^2$

An Eisenstein triple is related to 60 degree triangles and a special case of the cosine law. But we need not worry about that except to note that a specific example of an Eisenstein triple is $7^2 = 5^...
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3answers
2k views

Can you put L trominos to fill the figure?

In the above picture, there are 24 squares. Can you only use L trominos to fill the figure? If yes, give an example. Otherwise, please explain why. An L tromino is like this:
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2answers
204 views

Covering an 8x8 grid with W pentominoes

What is the minimum number of W pentominoes you need to cover every cell of an 8x8 grid? Pentominoes may overlap each other and sit outside the boundary of the grid. They can also be rotated in any ...
14
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6answers
2k views

Covering an 8x8 grid with X pentominoes

What is the minimum number of X pentominoes you need to cover every cell of an 8x8 grid? Pentominoes may overlap each other and sit outside the boundary of the grid. An X pentomino looks like this:
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4answers
167 views

Rectangles formed from every tetromino, tromino and domino

Can you form a 4x7 rectangle from every tetromino, tromino and domino? There are 5 different tetrominoes, 2 trominoes and 1 domino. Can you find different arrangements that are not mirrors/rotations ...
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3answers
319 views

Four hand tiled squares demonstrating a Pythagorean Quadruple

Demonstrating the Pythagorean Quadruple $6\times6 + 6\times6 + 7\times7 = 11\times11$ Using the pieces shown in the $11\times11$ square: The objective: Arrange the pink pieces (four enneominoes) ...
6
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1answer
245 views

Piece de Resistance - Eight Doubled Tetrominoes Make a Tetronogram

Eight Doubled Tetrominoes Make a Tetronogram This puzzle is part of the "Piece de Resistance" series. Go back to Part 1 (Ace) for the story.Ace Two Three Four Five Six Seven Eight ... Time for ...
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1answer
639 views

Introducing Tetronogram - Beginner's Version

Introducing Tetronogram! (named by @MrPie) The puzzle is made of a grid like a nonogram. Notations are along the axes like a classic nonogram but numbers are replaced by the names of the ...
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1answer
249 views

Restoring 3D Tetromino Puzzle

You won't believe this. I worked all night to make a new 3D tetromino puzzle, and just as I was about to save the final version there was a power outage! Now I can't remember what the final clues were ...
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1answer
311 views

3D tetromino placement

The following image depicts a $5\times5\times5$ cube. Insert any number of the pictured 3D-tetromino pieces into the cube to satisfy the conditions listed below. Pieces may be rotated in any direction....
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2answers
544 views

BOOM! All Clear for Mr. T

In Tetris 99, Mr. T loves performing All Clears, which happen when a piece clears all lines in the playing field. Being a gentleman, he also tries to minimize the total damage he sends to his ...
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2answers
388 views

Pentomino solution maximizing straight lines length in rectangle - wood cutter problem

Recently in my free time I cut from wood with my scroll saw two pentomino sets. One set made from 10x6 pattern, and then the other set 20x3 pattern. Think of wood cutter difficulties. I would like to ...
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1answer
1k views

How many colors does it take?

This question is from a popular monthly science magazine in my country: You have an 8x8 square where any 3 squares forming a tromino (including reflections and rotations) must consist of three ...
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2answers
826 views

The Pentomino Snake

The premise of the puzzle is quite simple. Here's how to set it up. Draw a 5x5 grid of squares. Write the number 1 in the middle. Make a "snake" of numbers up to 25 so that each number is ...
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1answer
229 views

Statue Park (Loop)

Place each of the twelve pentominoes into the grid once, with rotations and reflections allowed. No two pentominoes can overlap or be orthogonally adjacent, and all cells not occupied by the ...
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2answers
262 views

Tiling rectangles with a Heptomino plus 2x2 square

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
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2answers
178 views

Tiling rectangles with Heptomino plus rectangle #7

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...