Questions tagged [polyomino]

A geometric puzzle centered around geometric figures formed from unit-squares.

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39
votes
2answers
986 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 ...
17
votes
3answers
300 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,...
17
votes
1answer
483 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 ...
15
votes
2answers
659 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
397 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
353 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
599 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
507 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
3answers
835 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 ...
13
votes
1answer
336 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
903 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
557 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 ...
11
votes
2answers
488 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
754 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
507 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
257 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 ...
9
votes
3answers
537 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
2answers
834 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
446 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
506 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
222 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
201 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
453 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
482 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
278 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
240 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
175 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
172 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
1answer
201 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....
6
votes
2answers
144 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
242 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
667 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
232 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
230 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
176 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
540 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
503 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
435 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
191 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
147 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
120 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
130 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
88 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
188 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
134 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
127 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
145 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 ...