Questions tagged [polyomino]
A geometric puzzle centered around geometric figures formed from unit-squares.
72
questions
6
votes
0answers
89 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
248 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 ...
7
votes
1answer
221 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 ...
12
votes
2answers
279 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
337 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
votes
1answer
378 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 ...
15
votes
2answers
766 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 ...
7
votes
1answer
110 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
384 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
614 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
297 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^...
21
votes
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:
4
votes
2answers
190 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
152 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
305 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
223 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
605 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
230 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 ...
6
votes
1answer
279 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
535 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
316 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
805 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
1answer
218 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
238 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
168 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
...
11
votes
2answers
508 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 ...
5
votes
2answers
250 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
...
3
votes
2answers
166 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
2answers
150 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
102 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
1answer
142 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 ...
5
votes
1answer
268 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 ...
6
votes
1answer
186 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 ...
9
votes
3answers
612 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.
...
6
votes
3answers
322 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
255 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
...
3
votes
3answers
209 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
...
8
votes
2answers
252 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
...
7
votes
6answers
538 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
...
8
votes
3answers
612 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
...
14
votes
2answers
561 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
...
15
votes
1answer
440 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 ...
6
votes
2answers
163 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.
...
3
votes
1answer
126 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. ...
8
votes
3answers
216 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 ...
5
votes
1answer
217 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 ...
14
votes
2answers
392 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 ...
