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Questions tagged [polyomino]

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

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8
votes
2answers
245 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^...
20
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
167 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
125 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
288 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) ...
5
votes
1answer
181 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
555 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
207 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
239 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
520 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
266 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
690 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
211 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
210 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
154 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
493 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
240 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
150 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
136 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
94 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
132 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
242 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
181 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
553 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
294 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
245 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
196 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
231 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
469 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
502 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
527 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
412 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
147 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
121 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
203 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
184 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
364 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 ...
9
votes
2answers
529 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 ...
13
votes
3answers
843 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 ...
15
votes
2answers
688 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 ...
2
votes
2answers
143 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 ...
45
votes
3answers
3k views

Tiling with T-tetrominos in gravity

The goal is to tile all the white squares using T-tetrominos when there is gravity pulling the tetrominos downwards like regular tetris. The black squares are void and the ground is just below the ...
11
votes
2answers
758 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 ...
13
votes
1answer
340 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 ...
17
votes
3answers
307 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,...
4
votes
2answers
565 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 ...
9
votes
1answer
518 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 ...
4
votes
2answers
464 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 ...