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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13 votes
2 answers
456 views

Minimum lines needed to draw the 12 pentominoes

You need 4 lines to draw the monomino and the same for the domino You can draw the 2 trominoes with 7 lines For the five tetrominoes I could do it first with 16 lines Then 15 lines And my best try ...
Rodolfo Kurchan's user avatar
10 votes
3 answers
849 views

Fewest polyominoes adjacent to 3 copies

What is the smallest positive number of polyominoes P, such that You can place grid aligned copies of P without any overlap; and Each polyomino is adjacent to exactly 3 other polyominoes. ...
Dmitry Kamenetsky's user avatar
2 votes
3 answers
725 views

Smallest polyomino adjacent to 3 copies

What is the smallest polyomino P in number of cells, such that You can place grid aligned copies of P without any overlap; and Each polyomino is adjacent to exactly 3 other polyominoes. Polyominoes ...
Dmitry Kamenetsky's user avatar
6 votes
1 answer
295 views

The Nine Gardens Of Eden

This puzzle is part of the Monthly Topic Challenge #11: Now in 3D. There are nine distinct known three-cell Garden of Eden patterns in the Life Without Death cellular automata, including the two well-...
Scratch---Cat's user avatar
18 votes
1 answer
559 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
  • 75.6k
13 votes
1 answer
973 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
  • 75.6k
8 votes
4 answers
877 views

Smallest rectangle to put the 24 ABCD words combination

Put in the smallest possible size board all combination of 4 quantity of letters. Crossword must be connected. And can be only 4 letters words. Cannot be words with 2, 3, 5 or more letters Example for:...
Rodolfo Kurchan's user avatar
17 votes
3 answers
1k views

Most polyominoes in an 8x8 grid

What is the most number of distinct free polyominoes you can form by painting an 8x8 grid in two colours? Here a polyomino is a set of orthogonally adjacent cells of the same colour, so polyominoes of ...
Dmitry Kamenetsky's user avatar
3 votes
3 answers
1k 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
  • 49
10 votes
1 answer
446 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
  • 75.6k
6 votes
0 answers
195 views

Set of magic polyominoes that can tile a square

Let's first look at this square grid of numbers. The 9 squares in yellow is what we are looking at and the green numbers are the sums for the digits within the rows and columns. The red squares are ...
Maff's user avatar
  • 601
7 votes
2 answers
288 views

Polyominos packing into a square

Rules of the game: Take a square grid nxn. Populate the grid with polyonimoes of area size 1 to area of 9. Polyominoes can be any shape. There must be one each of every size polyomino in every row ...
Maff's user avatar
  • 601
9 votes
1 answer
369 views

"Symmetric" Tetrikabe

This puzzle's theme is inspired by one from Grandmaster Puzzles' "The Art of Puzzles", but the puzzle itself is original. Rules: (Nurikabe section shamelessly stolen from an earlier puzzle ...
bobble's user avatar
  • 10.1k
9 votes
1 answer
535 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
  • 75.6k
24 votes
1 answer
1k views

The woefully underclued crossword

This puzzle is part of the Monthly Topic Challenge #4: Cross-*non*-words Giving clues for everything makes things way too simple. In this crossword, four clues are not given and you must find a way ...
Jafe's user avatar
  • 75.6k
3 votes
0 answers
220 views

Cover a 15×8 board with the pentominoes [closed]

Cover the entire area of the 15×8 square shape with two complete sets of 12 different types of pentominoes. The pentominos can be rotated and flipped. Two pentominoes of the same type must not be ...
Bill's user avatar
  • 31
13 votes
4 answers
759 views

What approach can I use to solve this wooden packing puzzle?

I am looking for an approach to solve a wooden packing puzzle which my three-year-old got as a present. We enthusiastically unpacked and disassembled the puzzle when she got it. (It came put-together ...
justfortherec's user avatar
6 votes
1 answer
659 views

Solving a 5x5 pentomino with only certain shapes

I have a physical Pentomino puzzle lying around, which contains 2 F pieces, one Y piece, one T piece and one W piece. The area into which the squares are supposed to fit in is just a little under 6 ...
Cheese Macken's user avatar
7 votes
1 answer
252 views

Shaka/shawaka: Trominoes

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
  • 75.6k
8 votes
2 answers
344 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
  • 75.6k
8 votes
1 answer
503 views

Pentomino - is there any solution with the straight-bar piece in the middle of a rectangle?

Is there a solution for a straight-bar piece not touching the edge of the rectangle? By rectangle solution, I mean either one of the patterns 15x4, 12x5, or 10x6. By straight-bar piece, I mean the ...
Przemyslaw Remin's user avatar
39 votes
6 answers
2k views

Packing pentominoes in a circle

You want to prepare a pizza of 12 flavors. You have 12 oddly-shaped pieces of cheese that you decide to use for the pizza. The shapes happen to be ... Oh, well, forget it! This isn't going to be ...
Florian F's user avatar
  • 26.4k
-2 votes
1 answer
156 views

15 x 15 polyomino

You cannot move the red squares You cannot rotate the blocks You cannot have 2 block of the same color touching each other, not even diagonally (by their corners) Grey blocks cannot touch a red square,...
Alain Reve's user avatar
3 votes
1 answer
201 views

Block fill in date puzzle

I have been trying this puzzle for HOURS!!! The goal is the fit all the pieces but not cover Aug or 1. You can rotate the pieces. Credit to www.dragonfjord.com The link shown at the bottom of the ...
Slayveer's user avatar
2 votes
1 answer
106 views

Tiling with dominoes then with tetrominoes

For reference, here are the five tetrominoes: Suppose you join ten dominoes to make a polyomino made of twenty unit squares. Is it possible that you can tile the polyomino using all the five given ...
Will Octagon Gibson's user avatar
8 votes
1 answer
478 views

Tiling a 5x5 square with five pentominoes AND a Latin square

Suppose that a 5x5 square has been tiled with five (not necessarily distinct) pentominoes. Is it true that there will necessarily exist at least one Latin square of size 5x5 (using the numbers 1,2,3,...
Will Octagon Gibson's user avatar
20 votes
3 answers
2k views

The universal ticket

I am submitting a very interesting problem from a French mathematical recreation site: http://www.diophante.fr/problemes-par-themes/g-probabilites/g2-combinatoire-denombrements/1434-g248-le-billet-...
franck vivien's user avatar
3 votes
2 answers
392 views

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 ...
Dmitry Kamenetsky's user avatar
3 votes
3 answers
517 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 ...
Dmitry Kamenetsky's user avatar
8 votes
1 answer
211 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 (...
hexomino's user avatar
  • 132k
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
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) ?
Dmitry Kamenetsky's user avatar
11 votes
1 answer
1k 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 ...
mafu's user avatar
  • 299
3 votes
1 answer
343 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 ...
user21820's user avatar
  • 1,115
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
2 votes
1 answer
233 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
2 answers
187 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 ...
Dmitry Kamenetsky's user avatar
2 votes
1 answer
216 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, ...
Parcly Taxel's user avatar
  • 6,954
6 votes
2 answers
458 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? ...
Allure's user avatar
  • 163
9 votes
2 answers
516 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. ...
Bubbler's user avatar
  • 11.5k
11 votes
1 answer
240 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 ...
Parcly Taxel's user avatar
  • 6,954
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 ...
Stiv's user avatar
  • 129k
15 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 ...
Wheat Wizard's user avatar
  • 1,293
-1 votes
2 answers
204 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 ...
Vassilis Parassidis's user avatar
6 votes
2 answers
256 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 ...
Dmitry Kamenetsky's user avatar
2 votes
1 answer
105 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?
Dmitry Kamenetsky's user avatar
2 votes
1 answer
290 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
1 vote
3 answers
301 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 ...
IsaacRoan Sison's user avatar
1 vote
1 answer
93 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 ...
DRA's user avatar
  • 21
23 votes
1 answer
960 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
  • 129k