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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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8 votes
3 answers
752 views

Tiling rectangles with F pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with N pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
theonetruepath's user avatar
26 votes
5 answers
2k views

Polyomino T hexomino and rectangle packing into rectangle

Let's pack some (one or more) T hexominoes together with some (one or more) small $a\times b$ rectangles into some bigger $m\times n$ rectangle without holes and overlapping pieces. For example, I ...
Somnium's user avatar
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9 votes
5 answers
1k views

Polyomino Z pentomino and rectangle packing into rectangle

See my similar question about T hexomino (Polyomino T hexomino and rectangle packing into rectangle) This is exactly same but with other polyomino - Z pentomino. Let's pack some (one or more) Z ...
Somnium's user avatar
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6 votes
3 answers
444 views

Tiling rectangles with X pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
theonetruepath's user avatar
5 votes
1 answer
319 views

Tiling rectangles with Hexomino plus rectangle #1

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 Next ...
theonetruepath's user avatar
14 votes
2 answers
717 views

Tiling rectangles with W pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
theonetruepath's user avatar
9 votes
2 answers
307 views

Tiling rectangles with T pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
theonetruepath's user avatar
7 votes
6 answers
616 views

Tiling rectangles with N pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
theonetruepath's user avatar
6 votes
2 answers
314 views

Tiling rectangles with V pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
theonetruepath's user avatar
4 votes
3 answers
320 views

Tiling rectangles with U pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
theonetruepath's user avatar
6 votes
1 answer
289 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 ...
Omega Krypton's user avatar
267 votes
1 answer
31k views

Is this Tetris puzzle solvable?

As a birthday present last year, I received some fridge magnets. They didn't come as a puzzle, so I don't know if they have a solution, but I made a puzzle out of them anyway. The magnets are ...
James Webster's user avatar
16 votes
6 answers
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:
Dmitry Kamenetsky's user avatar
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 ...
Ignac's user avatar
  • 141
26 votes
3 answers
3k 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:
Culver Kwan's user avatar
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14 votes
2 answers
1k views

Find smallest rectangle divided into figures so each figure has 5 neighbours

The following 3x4 rectangle can be cut into pieces along grid lines, so that each piece has exactly three neighbors: Problem: Find the smallest rectangle on the integer grid that can be cut into ...
Somnium's user avatar
  • 1,028
13 votes
1 answer
536 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 ...
bobble's user avatar
  • 10.4k
12 votes
2 answers
456 views

A Crabby Sudoku

I present a *deep breath* Even-Odd TetroThermoDoku. From the back of the name to the front: Rules Sudoku: Fill each cell with a digit 1-9 such that no number repeats in any row, column, or 3x3 heavy-...
bobble's user avatar
  • 10.4k
5 votes
2 answers
291 views

Tiling rectangles with Heptomino plus rectangle #6

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 ...
theonetruepath's user avatar
3 votes
2 answers
176 views

Tiling rectangles with Heptomino plus rectangle #4

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 ...
theonetruepath's user avatar
2 votes
2 answers
136 views

Tiling rectangles with Hexomino plus rectangle #2

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 ...
theonetruepath's user avatar
2 votes
1 answer
325 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 ...
Vassilis Parassidis's user avatar
1 vote
2 answers
264 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 ...
theonetruepath's user avatar
42 votes
2 answers
1k views

Dissecting Africa

A straightforward puzzle for the patient. There are no tricks or decryptions needed. The task is 'simple' albeit potentially challenging (and maybe time-consuming). The goal Dissect the Africa-...
BmyGuest's user avatar
  • 18.2k
23 votes
1 answer
987 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 ...
Stiv's user avatar
  • 145k
18 votes
1 answer
601 views

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 ...
Jafe's user avatar
  • 77.8k
15 votes
2 answers
1k views

Tetromino Sudoku

An entry in Fortnightly Topic Challenge #32: Grid Deduction Hybrids The grid below, when filled in, forms a valid Sudoku grid. It can also be filled in like a LITS (nuruomino) puzzle without the 1x4 ...
MikeQ's user avatar
  • 6,830
15 votes
2 answers
526 views

Hexominoes into 7 simultaneous congruent shapes

I came up with this puzzle 16 years ago, it was on Ed Pegg's Mathpuzzle site but nobody solved it AFAIK. The 35 hexominoes (which look like this): are to be arranged, in groups of five, into seven ...
theonetruepath's user avatar
13 votes
1 answer
1k views

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 ...
Jafe's user avatar
  • 77.8k
13 votes
2 answers
762 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) ...
bobble's user avatar
  • 10.4k
13 votes
2 answers
642 views

Ziggy - Make a square from 8 polyomino pieces

A few years ago I created a small packing puzzle that I'd like to share here today. The puzzle is based on the fact that $1+2+3+4+5+6+7+8 = 6^2$. It consists of 8 zig-zag polyomino pieces, ranging in ...
Jaap Scherphuis's user avatar
12 votes
3 answers
1k views

Tiling a 5-by-5 bathroom with L-shaped triomino tiles

The following puzzle appeared in the Cambridge, UK February 2024 MathsJam Shout: Tiling with Triominoes Imagine tiling a 5-by-5 bathroom with L-shaped triomino tiles. Clearly, not every square can be ...
Will.Octagon.Gibson's user avatar
12 votes
2 answers
566 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 ...
Przemyslaw Remin's user avatar
12 votes
3 answers
1k views

Dissecting a square

You are asked to dissect an $N \times N$ square into polyomino pieces such that each piece shares a portion of its boundary with exactly $D$ other pieces, and no piece has area exceeding $N$. This can ...
Johannes's user avatar
  • 4,400
11 votes
3 answers
1k 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 ...
Dmitry Kamenetsky's user avatar
11 votes
1 answer
440 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 ...
bobble's user avatar
  • 10.4k
10 votes
1 answer
499 views

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 ...
Jafe's user avatar
  • 77.8k
10 votes
3 answers
908 views

Tiling a rectangle with just the Y pentomino

Inspired by this question series, which was inspired by this question. They give rise to beautiful pictures (at least in the eye of the beholder mathematician) and some nice generalizable solutions. ...
Glorfindel's user avatar
  • 28.1k
9 votes
1 answer
594 views

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 ...
Jafe's user avatar
  • 77.8k
9 votes
2 answers
720 views

Tetromi-nuri-doku

Note: This puzzle was inspired by the one here, by Mike Q. Every square in the grid above, when the puzzle is complete, has a number between 1 and 9 in it and either is shaded or is not. Each 3x3 ...
P...'s user avatar
  • 517
8 votes
3 answers
254 views

Hand tiling puzzle

Here's a set of polyominoes (sizes 4,5,6,7,8,9,10) that you can print and cut out. You can use the two smallest to make a 3x3. Nice easy one to get you started. Add a piece to make a 3x5. Add another ...
theonetruepath's user avatar
8 votes
2 answers
355 views

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 ...
Jafe's user avatar
  • 77.8k
8 votes
1 answer
472 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....
Jafe's user avatar
  • 77.8k
5 votes
3 answers
2k views

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...)
Daniel's user avatar
  • 69
4 votes
2 answers
207 views

Tiling rectangles with Hexomino plus rectangle #3

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 ...
theonetruepath's user avatar
4 votes
1 answer
300 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 ...
Vassilis Parassidis's user avatar
3 votes
3 answers
617 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?
Dmitry Kamenetsky's user avatar
2 votes
1 answer
334 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 ...
sunnyshi's user avatar
2 votes
1 answer
242 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 ...
Dmitry Kamenetsky's user avatar
2 votes
1 answer
169 views

Tiling rectangles with Heptomino plus rectangle #3

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 Next ...
theonetruepath's user avatar