# Questions tagged [polyomino]

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

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### 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:
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### 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:
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### 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 ...
308 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,...
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 ...
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### 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. ...
413 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 ...
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 ...
232 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 ...
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### 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 ...
296 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 ...
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. ...
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### 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. ...
204 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 ...
186 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
144 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 ...