It isn't trivial!—Livio Zucca
From 1999 to 2005 Livio Zucca maintained a vast website of mathematical
recreations called Remembrance of Software Past.
It was full of new ideas, attracting contributions from
many talented mathematicians.
Unfortunately, it was hosted by GeoCities,
which was shut down in 2009.
Fortunately Giovanni Resta reconstructed Remembrance
in full on his host
Iread.it.
Deteriorating eyesight left Livio unable to maintain his site.
With Livio's permission I have revived his Remembrance
pages
about polyomino compatibility.
I have updated the links and many of the solutions.
Livio and I welcome new contributions.
If you would like to submit an improved solution, or a new solution,
or a new idea, please write me at colonel@monmouth.com.
 | Pento-Tro-Dominoes. Find a figure that can be tiled with any of a given pentomino, tromino, and domino. |
 | Pento-Tetro-Trominoes. Find a figure that can be tiled with any of a given pentomino, tetromino, and tromino. |
 | Tetrominoes Challenge. Find a figure that can be tiled with each of a given set of tetrominoes and no others. |
 | Triple Pentominoes. Find a figure that can be tiled with each of three given pentominoes. |
 | Pentomino Odd Pairs. Find a figure that can be tiled with an odd number of either of two pentominoes. |
No room! No room!they cried out when they saw Alice coming.
The exclusion problem is to remove as few cells as possible from a given figure or the plane so as to exclude a given polyform.
 | Hexomino Exclusion. Exclude a hexomino from a checkerboard. |
 | Polyiamond Exclusion. Exclude a polyiamond from the plane. |
 | Polyhex Exclusion. Exclude a polyhex from the plane. |
The tiling problem is to join copies of one or more polyforms to make a given polyform.
 | Polyiamond Hexagon Tiling. Tile a straight or ragged hexagon with various polyiamonds. |
 | Tetrads. A polyform tetrad is four copies of a polyform, joined so every copy shares a boundary with every other. |
 | Pentomino Compatibility. Given two pentominoes, construct a figure that can be tiled with either. |
 | Holeless Hexomino Compatibility. Given two hexominoes, construct a holeless figure that can be tiled with either. |
 | Tetromino-Pentomino Compatibility. Given a tetromino and a pentomino, construct a figure that can be tiled with either. |
 | Holeless Tetromino-Hexomino Compatibility. Given a tetromino and a hexomino, construct a holeless figure that can be tiled with either. |
 | Holeless Pentomino-Hexomino Compatibility. Given a pentomino and a hexomino, construct a holeless figure that can be tiled with either. |
 | Square Enneiomino Compatibility. Which polyominoes are compatible with the square enneiomino? |
 | Voided Square Octomino Compatibility. Which polyominoes are compatible with the square octomino with a hole in it? |
 | Holeless Triple Pentominoes. Holeless solutions for Livio Zucca's Triple Pentominoes. |
 | Holeless Pentomino Odd Pairs. Holeless solutions for Livio Zucca's Pentomino Odd Pairs. |
 | Pentomino Odd Triples. Like Livio Zucca's Triple Pentominoes, with an odd number of tiles. |
 | Multiple Polyomino Compatibility. Figures that can be tiled by many polyominoes of the same order. |
 | Hexiamond Compatibility. Given two hexiamonds, construct a figure that can be tiled with either. |
 | Triple Hexiamonds. Given three hexiamonds, construct a figure that can be tiled with each. |
 | Heptiamond Compatibility. Given two heptiamonds, construct a figure that can be tiled with either. |
 | Octiamond Compatibility. Given two octiamonds, construct a figure that can be tiled with either. |
| Mixed Polyiamond Compatibility. Given two polyiamonds of different orders, construct a figure that can be tiled with either. |
 | Multiple Polyiamond Compatibility. Figures that can be tiled by many polyiamonds of the same order. |
 | Pentahex Compatibility. Given two pentahexes, construct a figure that can be tiled with either. |
 | Pentahex Odd Pairs. Given two pentahexes, construct a figure that can be tiled with an odd number of either. |
 | Mixed Polyhex Compatibility. Given two polyhexes of different orders, construct a figure that can be tiled with either. |
 | Seven Euphoric Pentahexes. Each of these pentahexes is compatible with all 82 hexahexes. |
 | Three Euphoric Hexahexes. Each of these hexahexes is compatible with all 82 hexahexes. |
 | Ring Hexahex Compatibility. Which polyhexes are compatible with the ring hexahex? |
 | Multiple Polyhex Compatibility. Figures that can be tiled by many polyhexes of the same order. |
 | Zucca's Challenge Problem for Tetrahexes. Given a set of tetrahexes, construct a figure that can be tiled with any member of the set and no other. |
 | Zucca's Challenge Problem. Given a set of polyforms of the same order, construct a figure that can be tiled with any member of the set and no other. |
 | Pentapent Compatibility. Figures that can be tiled by two different pentapents. |
 | Mixed Polypent Compatibility. Figures that can be tiled by polypents of different orders. |
 | Pentahept Compatibility. Given two pentahepts, construct a figure that can be tiled with either. |
 | Tetrabolo Compatibility. Given two tetraboloes, construct a figure that can be tiled with either. |
 | Tetrabolo-Pentabolo Compatibility. Given a tetrabolo and a pentabolo, construct a figure that can be tiled with either. |
 | Tetrahop Compatibility. Given two tetrahops, construct a figure that can be tiled with either. |
 | Tetracube Compatibility. Given two tetracubes, construct a figure that can be tiled with either. |
 | Pentacube Compatibility. Given two pentacubes, construct a figure that can be tiled with either. |
 | Cell Shifts for Polyominoes of order up through 6. |  | Cell Shifts for Pentomino Pairs. |
 | Cell Shifts for Polyhexes of order up through 5. |  | Cell Shifts for Pentahex Pairs. |
 | Cell Shifts for Heptominoes. |  | Cell Shifts for Hexahexes. |
 | Cell Shifts for Polyiamonds of order up through 7. |  | Cell Shifts for Heptahexes. |
 | Cell Shifts for Octiamonds. |
That is another of your odd notions,said the Prefect, who had the fashion of calling everything
oddthat was beyond his comprehension, and thus lived amid an absolute legion of
oddities.
The Purloined Letter
An oddity is a figure with binary symmetry made by joining an odd number of copies of a polyform.
 | Polyomino Oddities. Oddities for polyominoes of order up to 7. |
 | Pentomino Oddities. Pentomino oddities with specific symmetries. |
 | Hexomino Oddities. Hexomino oddities with specific symmetries. |
 | Polyomino Semi-Oddities. Semi-oddities for polyominoes. A semi-oddity is a figure with quaternary symmetry and an even number of tiles that is not a multiple of 4. |
 | Heptomino Oddities. Heptomino oddities with specific symmetries. |
 | Pentaking Oddities. Oddities with specific symmetries for pseudopolyominoes of order 5. |
 | Pentiamond, Heptiamond, and Enneiamond Oddities. Oddities for pentiamonds, heptiamonds, and enneiamonds. Oddities for polyiamonds of odd order can have only bilateral symmetry. |
 | Hexiamond Oddities. Hexiamond oddities with specific symmetries. |
 | Octiamond Oddities. Octiamond oddities with specific symmetries. |
 | Polyiamond Tri-Oddities. These are like oddities but with ternary symmetry. |
 | Polyhex Oddities. Oddities for polyhexes of order up to 5, with specific symmetries. |
 | Hexahex Oddities. Hexahex oddities with specific symmetries. |
 | Heptahex Oddities. Heptahex oddities with specific symmetries. |
 | Polyhex Tri-Oddities. Tri-oddities for polyhexes of order up to 5. |
 | Hexahex Tri-Oddities. Tri-oddities for hexahexes. |
 | Heptahex Tri-Oddities. Tri-oddities for heptahexes. |
 | Pentapent Oddities. Oddities for pentapents. |
 | Hexapent Oddities. Oddities for hexapents. |
 | Heptapent Oddities. Oddities for heptapents. |
 | Pentahept Oddities. Oddities for pentahepts. |
 | Polyoct Oddities. Oddities for polyocts of order 1 through 5. |
 | Pentenn Oddities. Oddities for pentenns. |
 | Polydec Oddities. Oddities for polydecs. |
 | Catalogue of Polypents. Enumerations and pictures of these neglected polyforms. |
 | Catalogue of Polyhepts. Some more neglected polyforms. |
 | Catalogue of Polyocts. Still more neglected polyforms. |
 | Catalogue of Polyhops. Thomas Atkinson's hopscotch-style polyominoes. |
 | Catalogue of Polyjogs. Polyforms formed of squares joined by half edges. |
 | Catalogue of Polypennies. Polyforms formed by joining disks tangentially. |
 | Polycube Symmetries. In how many ways can a polycube be symmetrical? |
 | Catalogue of Polyrhons. Polyforms formed by joining rhombic dodecahedrons. |
 | Printable Grid Files. Square, triangular, and hexagonal grids, for those who like to play with polyominoes, polyiamonds, and polyhexes. |
 | Tetromino Wallpaper. |
 | Pentiamond Wallpaper. |
 | Tetrahex Wallpaper. |
 | Dragomino Wallpaper. A Dragomino is the polyomino equivalent of a Dragon Curve. |
These roads are all strange—and what a lot of them there are!
| Livio Zucca's Remembrance of Software Past |
| Andrew Clarke's The Poly Pages |
| Polyiamonds, at Mathematische Basteleien (in German) |
| Miroslav Vicher's Polyiamonds Page |
| Iamonds at Ed Pegg's mathpuzzle.com |
| Polyominoes and Other Animals at The Geometry Junkyard |
| Polyiamond at MathWorld |
| Gabriele Carelli's Polyforms (in Italian) |
| The September 2004 issue of Erich Friedman's Math Magic, on polyform compatibility |
| The November 2004 issue of Erich Friedman's Math Magic, on Galvagni's Multiple Tiling Problem |
| Peter's Polyform Pages |
| Michael Reid's Polyomino Page |
| Giovanni Resta's Polypolyominoes |
| Jorge Luis Mireles's Poly2ominoes |
| KSO Glorieux Ronse's Pentomino site, established by Odette De Meulemeester |
| Rodolfo Marcelo Kurchan's periodical Puzzle Fun |
| K. Ishino's Puzzle Page (in Japanese) |
| Alexandre Owen Muñiz's Math at First Sight |
| Torsten Sillke's Home Page |
| Abaroth's Puzzles |
 | Many of my constructions were found using the computing resources of Netrics. |
