Questions tagged [polyomino]

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

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6
votes
1answer
247 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 ...
14
votes
3answers
604 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 ...
4
votes
3answers
552 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 ...
244
votes
1answer
25k views

Is this Tetris puzzle solvable?

As a birthday present last year, I received some fridge magnets. They didn't come as a puzzle, so I don't know if they have a solution, but I made a puzzle out of them anyway. The magnets are ...
0
votes
1answer
583 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....
39
votes
2answers
1k 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-...
8
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 ...
12
votes
2answers
571 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 ...
10
votes
2answers
860 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 ...
13
votes
2answers
915 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 ...
25
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 ...