Hexominoes: Puzzles & Solutions

Author: David Goodger <goodger@python.org>
Date: 2013-07-03
Revision: 585
Web site:http://puzzler.sourceforge.net/
Copyright: © 1998-2012 by David J. Goodger
License:GPL 2
images/puzzler.png

Contents

High-quality acrylic sets of hexominoes are available from Kadon Enterprises as Sextillions.

Hexominoes

Squares & Rectangles

Due to a parity imbalance, the 35 free hexominoes cannot fit into a simple rectangle without introducing holes or other irregularities.

Parallelograms

As demonstrated below, the 35 hexominoes can fit into parallelograms with odd-length bases. The parity imbalance that prevents simple rectangles also prevents solutions to parallelograms with even-length bases (e.g. 30x7 & 42x5).

Hexominoes-Plus

Also known as Kadon's Sextillions, these are the hexominoes with a second N06 ("short N") piece called S16 ("short S"), for a total of 36 pieces, avoiding the parity imbalance and allowing the construction of simple rectangles.

Misc

One-Sided Hexominoes

These are just like regular hexominoes, except that non-isomorphic reflections (different shape when flipped over) are treated as separate pieces, and pieces are not allowed to be flipped.

Cornucopia Puzzle

Invented by Stewart T. Coffin, this is a semi-arbitrary subset of the hexominoes. Many Cornucopia puzzles described in Coffin's Puzzling World of Polyhedral Dissections then only use a subset of this subset.

From the set of hexominoes,

eliminate all pieces having reflexive or rotational symmetry and all those containing a 2 x 2 square because they are less desirable for various reasons already explained. The remaining 17 pieces are the set of Cornucopia pieces.

The Puzzling World of Polyhedral Dissections, by Stewart T. Coffin

These are all the pieces listed in An Introduction to Polyominoes: Hexominoes with 8 aspects which do not contain 2x2 blocks. The Polyform Puzzler hexomino names of the pieces are listed under the first puzzle below.