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 |

Contents

- One-Sided Polytwigs of Order 1 Through 3
- Tetratwigs
- One-Sided Tetratwigs
- Polytwigs of Order 1 Through 4
- One-Sided Polytwigs of Order 1 Through 4
- Pentatwigs
- One-Sided Pentatwigs
- Polytwigs of Order 4 & 5
- Polytwigs of Order 1 Through 5
- One-Sided Polytwigs of Order 1 Through 5
- Hexatwigs
- One-Sided Hexatwigs
- Polytwigs of Order 1 Through 6
- Quasi-Tritwigs
- Quasi-Polytwigs of Order 1 Through 3

This puzzle uses the 1 monotwig, 1 ditwig, and 4 one-sided tritwigs,, for a total of 15 line segments on the hexagonal grid.

Triangle: 3 solutions

This puzzle uses the 4 tetratwigs for a total of 16 line segments on the hexagonal grid.

Arch: 2 solutions

These puzzles use the 6 one-sided tetratwigs for a total of 24 line segments on the hexagonal grid.

Triangles with 3 line segments omitted in various positions:

Arches with 2 line segments omitted in various positions:

These puzzles use the 1 monotwig, 1 ditwig, 3 tritwigs, and 4 tetratwigs, for a total of 28 line segments on the hexagonal grid.

Hexagons with 2 line segments omitted in various positions:

4x2 inset rectangle: 5,755 solutions

These puzzles use the 1 monotwig, 1 ditwig, 4 one-sided tritwigs, and 6 one-sided tetratwigs, for a total of 39 line segments on the hexagonal grid.

5x2 trapezoid: solutions incomplete

3x2 elongated hexagons with 2 segments omitted in various positions:

Triangles:

These puzzles use the 12 pentatwigs (a.k.a. pentacules), for a total of 60 line segments on the hexagonal grid.

Triangle: 56 solutions

Triangle variations (puzzle designs by Colin F. Brown):

5x3 parallelogram: 194 solutions

4x4 parallelograms:

6x3 trapezoid: 184 solutions

5x3 staggered rectangle: 145 solutions

5x3 wave-staggered rectangle (puzzle design by Colin F. Brown): 202 solutions

3x3 chevron: 115 solutions

5x2 chevron: 241 solutions

Butterfly: 8 solutions

Trefoil (puzzle design by Colin F. Brown): 4 solutions

If you look carefully, you can see that the solution above consists of 3 congruent shapes (in fact, all 4 solutions share this property). This is illustrated explicitly in the following exploded form (same 4 solutions, just rearranged):

Möbius strip (puzzle design by Colin F. Brown): 6 solutions?

Take the puzzle strip above, give one end a half-twist, and join it to the other end, resulting in a Möbius strip, a surface with only one side and one edge.

This puzzle was implemented without any coordinate "wrap-around": a piece cannot begin at the right edge and continue (through the join) to the left edge. There may be many more solutions with such a wrap-around configuration.

Elongated rounded rectangle (design by Colin F. Brown): 21 solutions

Rosette clusters (design by Colin F. Brown):

5x2 elongated hexagon (with holes; puzzle design by Colin F. Brown): 2 solutions

These puzzles use the 19 one-sided pentatwigs, for a total of 95 line segments on the hexagonal grid.

12x2 trapezoid: solutions incomplete

7x4 inset rectangle with 1 segment omitted in various positions:

8x2 elongated hexagons (with holes):

3x4 elongated hexagons (with holes):

String of rosettes (design by Peter F. Esser): solutions incomplete

Cross (design by Peter F. Esser): solutions incomplete

Peanuts:

These puzzles use the 4 tetratwigs and 12 pentatwigs, for a total of 76 line segments on the hexagonal grid.

Triangle: solutions incomplete

Diamond ring: solutions incomplete

4x3 elongated hexagon ring: solutions incomplete

5x3 butterfly ring: solutions incomplete

5x5 inset rectangle ring: solutions incomplete

Four congruent groups:

Colin F. Brown posed this problem: divide the twelve pentatwigs into four groups of three, add one of the tetratwigs to each group. Now find a 19-line region that each (equally divided) group will tile.

Mr. Brown provided one solution:

Others are possible:

**Open Problem: Combined Symmetrical Shape**Find a solution to the four congruent groups problem such that the four groups can be combined into a symmetrical shape. The more symmetries the better.

The best case I have been able to come up with so far:

These puzzles use the 1 monotwig, 1 ditwig, 3 tritwigs, 4 tetratwigs, and 12 pentatwigs, for a total of 88 line segments on the hexagonal grid.

5x5 inset rectangle: solutions incomplete

6x4 parallelograms with 3 segments omitted in various positions:

9x3 trapezoid ring: solutions incomplete

4x3 elongated hexagon with 1 segment omitted: solutions incomplete

8x2 butterfly with 2 segments omitted in various positions:

These puzzles use the 1 monotwig, 1 ditwig, 4 one-sided tritwigs, 6 one-sided tetratwigs, and 19 one-sided pentatwigs, for a total of 134 line segments on the hexagonal grid.

12x2 butterfly: solutions incomplete

12x3 parallelogram with 3 segments omitted in various positions:

13x3 trapezoid with 3 segments omitted in various positions:

These puzzles use the 27 hexatwigs, for a total of 162 line segments on the hexagonal grid.

Triangle: solutions incomplete

Triangle rings:

14x2 elongated hexagon: solutions incomplete

Hexagon rings:

Elongated hexagon ring (design by Peter F. Esser): solutions incomplete

6x3 semiregular hexagon: solutions incomplete

This solution was first found by Peter F. Esser.

Knobbed hexagon: solutions incomplete

X (designed for G4G10):

Trefoils:

These puzzles use the 49 one-sided hexatwigs, for a total of 294 line segments on the hexagonal grid.

Hexagon ring: solutions incomplete

This solution was first found by Peter F. Esser.

26x2 elongated hexagon (design by Peter F. Esser): solutions incomplete

These puzzles use the 1 monotwig, 1 ditwig, 3 tritwigs, 4 tetratwigs, 12 pentatwigs, and 27 hexatwigs, for a total of 250 line segments on the hexagonal grid.

22x2 elongated hexagon (design by Peter F. Esser): solutions incomplete

These puzzles use the 17 quasi-tritwigs, for a total of 51 line segments on the hexagonal grid. See Quasi-Polyforms in An Introduction to Polytwigs.

10x1 parallelogram (design by Colin F. Brown): solutions incomplete

6x2 parallelogram: solutions incomplete

Triangles:

Snowflakes:

2x3 elongated hexagons:

Trefoils:

These puzzles use the monotwig, the 3 quasi-ditwigs, 17 quasi-tritwigs, for a total of 58 line segments on the hexagonal grid. See Quasi-Polyforms in An Introduction to Polytwigs.

9x2 rounded rectangle: solutions incomplete

Hexagon rings:

5x3 parallelogram ring: solutions incomplete

6x3 trapezoid ring: solutions incomplete