Questions tagged [polyomino]
A geometric puzzle centered around geometric figures formed from unit-squares, or a puzzle that uses polyominoes as an integral part.
94
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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 ...
1
vote
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 ...
23
votes
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
votes
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 ...
14
votes
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
votes
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
votes
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 ...
3
votes
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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votes
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 ...
4
votes
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 ...
2
votes
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 ...
8
votes
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, ...
asked Nov 24 '20 at 0:38
Bernardo Recamán Santos
12.8k2 gold badges23 silver badges115 bronze badges
13
votes
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
votes
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
votes
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 ...
14
votes
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
votes
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
votes
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 ...
6
votes
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 ...
9
votes
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 ...
15
votes
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 ...
asked May 19 '20 at 17:36
Bernardo Recamán Santos
12.8k2 gold badges23 silver badges115 bronze badges
7
votes
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 ...
asked Apr 5 '20 at 21:22
Bernardo Recamán Santos
12.8k2 gold badges23 silver badges115 bronze badges
13
votes
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 ...
7
votes
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 ...
asked Mar 23 '20 at 16:12
Bernardo Recamán Santos
12.8k2 gold badges23 silver badges115 bronze badges
11
votes
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 ...
asked Mar 19 '20 at 3:01
Bernardo Recamán Santos
12.8k2 gold badges23 silver badges115 bronze badges
16
votes
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 ...
10
votes
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
votes
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
votes
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 ...
8
votes
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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votes
3answers
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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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votes
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
votes
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:
0
votes
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 ...
10
votes
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
votes
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 ...
19
votes
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 ...
8
votes
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 ...
7
votes
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....
11
votes
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 ...
11
votes
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 ...
10
votes
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 ...
5
votes
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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votes
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 ...
2
votes
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
...
1
vote
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
...
