Questions tagged [polyomino]
A geometric puzzle centered around geometric figures formed from unit-squares.
38
votes
2answers
911 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-...
24
votes
5answers
1k 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 ...
16
votes
3answers
288 views
Pairs of Pairs of Pentominoes
Split the 12 pentominoes into three sets of four. Can you pair up pentominoes so that each set makes two of the same shape?
For instance, one of your three sets could look like this:
That uses the L,...
15
votes
2answers
615 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 ...
15
votes
1answer
357 views
Covering an 8×8 grid with trominoes
I tried to find non-trivial solutions on a deficient 8×8 grid covered with trominoes and I regret to say that after extensive efforts I found only two non-trivial solutions:
The conditions of ...
14
votes
2answers
335 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 ...
14
votes
3answers
587 views
ABC - A Blokus Commitment
Welcome to Blokus, a board game where you can place pieces of 1 to 5 blocks on a square board.
Each player has at his disposal every piece from monomino to pentomino.
A player's inventory is ...
14
votes
2answers
486 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
...
13
votes
1answer
328 views
Four Birds + One
You have a 7x7 tray, and several pieces as shown (the dimensions should be fairly obvious since the picture is to scale, but if not, a yellow bird piece fits snugly in a 4x4 square, the blue piece is ...
12
votes
2answers
887 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 ...
12
votes
2answers
767 views
Near-fill with 3x1 long triominos, how to do a different void square than the center square?
It's rather easy to fill a $7 \times 7$ board with 16 long triominos, leaving the center square void: see the picture below. But if I want to move the void square in another position, where else could ...
11
votes
2answers
476 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 ...
11
votes
2answers
745 views
What the L are they trying to prove?
Seems some L
t rominoes
have developed a punk attitude
and feel they have something to prove
because people always play with dominoes instead.
They are even jealous of I trominoes,
who ...
11
votes
2answers
515 views
Polyominoes on a checkerboard
Professor Halfbrain has spent his entire weekend by cutting lots of wooden $50\times50$ checkerboards into lots of polyominoes.
He looked at various pattern polyominoes with area $49$, and always ...
9
votes
3answers
463 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.
...
9
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 ...
9
votes
2answers
793 views
Dissecting a square
You are asked to dissect an $N \times N$ square into polyomino pieces such that each piece shares portion of its boundary with exactly $D$ other pieces, and no piece has area exceeding $N$. This can ...
9
votes
1answer
351 views
Pentominoes On the Edge
Source
Introducing Pentominoes!
It's the same concept as tetrominoes except they use 5 tiles instead of 4. Discounting rotations and reflections, there are 12 different free pentominoes. (If you ...
9
votes
2answers
176 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 ...
9
votes
2answers
476 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 ...
8
votes
2answers
206 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
...
8
votes
3answers
195 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 ...
7
votes
5answers
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 ...
7
votes
6answers
430 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
...
7
votes
3answers
438 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
...
6
votes
3answers
256 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
...
6
votes
2answers
232 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
...
6
votes
1answer
165 views
Tiling a rectangle with an odd number of Y pentomoes
Follow-on from Tiling a rectangle with just the Y pentomino
Two questions:
Find the smallest rectangle that can be tiled with an odd number of
Y pentominoes, or prove it impossible
Find the smallest ...
6
votes
2answers
137 views
Four Pieces Polyomino
Goal: Create a symmetric polyomino using:
Two pieces
Three pieces
All four pieces
Notes: This is the only set of four different pentominoes which has only one solution with 2, 3 and 4 pieces.
...
6
votes
1answer
228 views
A Blokus Flow problem
When I'm fed up with the usual rules of the boardgame Blokus, I'm making variations of it.
Here is one I recently come up with.
Provided on a blokus board, each player has at his disposal every ...
5
votes
2answers
646 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 ...
5
votes
2answers
226 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
...
5
votes
1answer
218 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 ...
5
votes
1answer
161 views
A minor rearrangement of the one sided hexominoes in 12 simultaneous shapes
Here are the one sided hexominoes arranged into 12 congruent shapes. But there are one or two flaws: The dark blue hexominoes, which are the symmetric ones, may not occur more than once each in a ...
4
votes
3answers
523 views
What is the largest, compact connected-network polyomino for these tiles?
This is a graphical arrangement puzzle. Consider the following 36 tiles:
Each tile has up to 8 connected directions and each tile has an initial up side. (The edge to whose centre the central ...
4
votes
2answers
385 views
Split the Pentominoes
Source
The image below shows a solved pentomino puzzle in a $6\times10$ grid.
Your challenge is to divide the rectangle along the black lines only to make two pieces that can be rearranged and fit ...
4
votes
2answers
352 views
Puzzle that consists of all possible combinations of pieces containing 5 squares
When I was a child my father gave me a wooden puzzle that consisted of pieces that represented every possible combination of 5 squares.
The goal was to arrange the pieces in various rectangular ...
3
votes
3answers
182 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
...
3
votes
2answers
134 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
...
3
votes
1answer
117 views
Hand tiling puzzle 2
Here's another set of polyominoes (sizes 4,5,6,7,8,9,10) that you can print and cut out. As before, the two smallest (same pieces as previous version) make a 3x3. The rest of the pieces are different. ...
3
votes
2answers
121 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
...
2
votes
2answers
84 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
...
2
votes
2answers
171 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
...
2
votes
2answers
120 views
Similar Polyomino Constructions
As you most likely already know, a polyomino is a polygon that you get by joining unit squares together in such a way that each edge of a unit square touching another unit square touches exactly one ...
2
votes
1answer
120 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 ...
1
vote
2answers
126 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
...
0
votes
1answer
450 views
What would be the most efficient algorithm to solve a polynomino?
From the 1970s I have a Hexomino called
Computer Puzzle in Computer Age
promising more than 1.000.000 solutions. A later version with a different title (I could not remember) says more than 1.000....
-5
votes
1answer
145 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 ...
