Hexiamonds: Puzzles & Solutions

Author: David Goodger <goodger@python.org>
Date: 2015-03-09
Revision: 612
Web site:http://puzzler.sourceforge.net/
Copyright: © 1998-2015 by David J. Goodger
License:GPL 2
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Contents

Hexiamonds

The free hexiamonds consist of 12 6-triangle polyforms, for a total of 72 unit triangles.

Parallelograms

Chevrons

Hexagons & Variants

"Choose 9" Hexagons

Puzzles that use 9 of the 12 hexiamonds to form an regular hexagon of side length 3.

Naively, there are (12 choose 9) = 220 different sets of 9 hexiamonds. However, to form a regular hexagon, an equal number of 'up' and 'down' triangles are necessary. The F6 & P6 hexiamonds are unbalanced (two 'up' triangles and four 'down', or vice-versa), while all other hexiamonds are balanced (three of each). So puzzles must either include or exclude both F6 & P6. Therefore there are actually (10 choose 3) + (10 choose 1) = 120 + 10 = 130 possible hexiamond subsets for these puzzles.

Which 9 hexiamonds to choose? Here are some ideas.

  • Hexicator: The "Hexicator" is Col. George L. Sicherman's puzzle consisting of 9 hexiamonds (the club/crook/J6, pistol/signpost/H6, and shoe/hook/G6 pieces are omitted) to be formed into a regular hexagon (side length 3). Try it before you look at the 1 and only solution (picture here).

    Perhaps this was the first set of 9 pieces that Col. Sicherman found that can make a hexagon in only one way. Is it the only set?

  • Choose-9 Hexagon 2: The pieces omitted from this puzzle are the three hexiamonds that cannot be formed with two triamonds: E6/crown, H6/pistol/signpost, and V6/lobster.

    Suggested by Michael Spencer on 2013-11-24:

    My local cafe has a wooden hexiamond puzzle that I thought might interest you. It is very similar to one puzzle you mention [Hexicator] but instead of omitting the G, H and J pieces it omits E, H and V (in other words, precisely those pieces that cannot be formed from two triamonds). I am now very curious to know how many solutions this version has!

    9 solutions

    images/iamonds/hexiamonds-choose-9-hexagon-2.png
  • Choose-9 Hexagon 3: The pieces omitted from this puzzle are the three hexiamonds that cannot be formed with three diamonds: F6/yacht, P6/sphinx, and X6/butterfly.

    15 solutions

    images/iamonds/hexiamonds-choose-9-hexagon-3.png

Hexagon-Grid Shapes

Miscellaneous

One-Sided Hexiamonds

The one-sided hexiamonds consist of 19 6-triangle polyforms, for a total of 114 unit triangles.

Hexagons & Variants

Hexagon-Grid Shapes

These shapes are all based on the hexagonal grid, made up of 19 6-triangle hexagons.

Miscellaneous