Pentahexes: Puzzles & Solutions
| Author: | David Goodger <goodger@python.org> |
|---|---|
| Date: | 2015-02-24 |
| Revision: | 600 |
| Web site: | http://puzzler.sourceforge.net/ |
| Copyright: | © 1998-2015 by David J. Goodger |
| License: | GPL 2 |
Pentahexes
There are 22 pentahexes totalling 110 unit hexagons.
Parallelograms
10x11 parallelogram: solutions incomplete
5x22 parallelogram: solutions incomplete
Trapezoids
15x11 trapezoid: solutions incomplete
5x24 trapezoid: solutions incomplete
Hexagons
A minimal regular hexagon comprises 127 unit hexagons, 17 units too large for the pentahexes, requiring holes:
Triangles
A minimal triangle is 120 units, 10 units too large. But 10 units makes a 4-unit-side triangle, so here are five variations with centered 4-unit triangular holes and one with a different hole:
Two length-10 triangles add up to the right number of unit hexagons: solutions incomplete
If the two triangles are pushed together, solutions to this puzzle are also solutions to the 10x11 parallelogram.
This design by Christoph M. Hoffman appeared in Martin Gardner's "Mathematical Games" column, Scientific American, June 1967.
Hexagrams
A minimal hexagram is 121 units, 11 units too large. These are variations with centered, symmetrical 11-unit holes:
One-Sided Pentahexes
Triangle: solutions incomplete
18x15 trapezoid: solutions incomplete
20x11 trapezoid: solutions incomplete
21x10 trapezoid: solutions incomplete
30x6 trapezoid: solutions incomplete
