Polyiamonds: Puzzles & Solutions
| Author: | David Goodger <goodger@python.org> |
|---|---|
| Date: | 2019-10-02 |
| Revision: | 657 |
| Web site: | http://puzzler.sourceforge.net/ |
| Copyright: | © 1998-2015 by David J. Goodger |
| License: | GPL 2 |
Contents
Polyiamonds of Order 1 Through 5
These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 3 tetriamonds, and 4 pentiamonds, for a total of 38 equilateral triangles.
9x1 elongated hexagon: 23,168 solutions
5x2 elongated hexagon ring (design by Dan Klarskov): 6,852 solutions
Stacked 5x1 elongated hexagons (suggested by Dan Klarskov):
10x1 butterfly: 2,000 solutions
Trapezoid: 98,807 solutions
Irregular hexagon (design by Dan Klarskov): 611,834 solutions
Peanut (2x3 elongated hexagon with side corners omitted; design by Dan Klarskov): 240,892 solutions
Snowflakes:
6,757 solutions (design by Dan Klarskov)
Dan's menagerie (animal designs by Dan Klarskov)
Bat: 61,251 solutions
Snake: 2,268 solutions
Bird: 42,665 solutions
Crab: 8,698 solutions
Dog: 28,614 solutions
X (designed for G4G10): 1,182 solutions
Elongated hexagons on hexagons:
2,810 solutions (design by Dan Klarskov)
Hexagons with 2×1 semi-regular hexagon holes (the same as in Kadon's Iamond Ring puzzle below):
One-Sided Polyiamonds of Order 1 Through 5
These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 4 one-sided tetriamonds, and 6 one-sided pentiamonds, for a total of 52 equilateral triangles.
4x2 semi-regular hexagon: 56,524,164 solutions
Hexagons with two unit-triangle holes:
X (designed for G4G10): 142,128 solutions
Polyiamonds of Order 1 Through 6
These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 3 tetriamonds, 4 pentiamonds, and 12 hexiamonds, for a total of 110 equilateral triangles.
3x5 elongated hexagon: solutions incomplete
11x5 parallelogram: solutions incomplete
8x5 butterfly: solutions incomplete
One-Sided Polyiamonds of Order 1 Through 6
These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 4 one-sided tetriamonds, 6 one-sided pentiamonds, and 19 one-sided hexiamonds, for a total of 166 equilateral triangles.
11x1 semi-regular hexagon: solutions incomplete
Triangles:
Polyiamonds of Order 1 Through 7
These puzzles use the 1 moniamond, 1 diamond, 1 triamond, 3 tetriamonds, 4 pentiamonds, 12 hexiamonds, and 24 heptiamonds, for a total of 278 equilateral triangles.
Hexagons:
Kadon's "Iamond Ring": solutions incomplete
The configuration above has the order 1 through 5 polyiamonds (moniamond, diamond, triamond, tetriamonds, & pentiamonds) restricted to an inner ring; the hexiamonds restricted to an intermediate ring; and the heptiamonds restricted to an outer ring. The coloured version below shows the moniamond in black, the diamond in gray, the triamond in purple, the tetriamonds in blue, the pentiamonds in green, the hexiamonds in red, and the heptiamonds in orange.
2x10 elongated hexagon: solutions incomplete
12x10 butterfly: solutions incomplete
