octiamonds and beyond

Border Patrol (TM) -- The Octiamond Set that fits in your pocket.

To order, see my Orders Page.  For smaller iamonds, visit my iamonds page.  Or go back to my Home Page.  Many puzzles can be made with them.

With pieces 13 27 22 46 45 30 33 55 32 60 63 52, make a figure with 4 sides.
With pieces  11 50 57 4 36 41 59 12 30 21 56 40 51 52 64, make a triangle with a hole at the center.
 The following diagram shows Michael Dowle's numbering system.  Piece 4and pieces 46-66 are unbalanced when colored .  Except for piece 4, all pieces 1-41 can be made with four diamonds.

The Border Patrol Octiamond set.  Solution and numbering by Michael Dowle.
With the octiamonds, you can play the wonderful game Border Patrol, created in a flash of inspiration by Adrienne Siskind.  For those that have the set, here is an alternate way to pack them in the box (solution by David Bird).  Each of these makes a hard puzzle.
44 57 62 41 53  12 33 35 55 48 60
10 27 4 16 36 46 61  3 34 15 63 11 42 19 2 43 54 23 28 56  9 17
13 31 58 66 14 22 37 39 45 32 26 38 1 59  6 29 30 20 21  8 25 64 50 7  5 24 47 49 18 40 51 52 65

There are trillions of puzzles that can be made with these pieces.  Draw 8 pieces at random, and make the figure with the fewest sides.  Here's another -- using the tetradiamonds, make a hexagon with sides (8 6 8 8 6 8).  The following is the (4 18 4 4 18 4) hexagon by Michael Dowle -- the first publication of a tetradiamond construction.

Tetradiamond Hexagon by Michael Dowle

The 66 Octiamonds are my favorite puzzle set.  During the 1999 National Puzzler's League convention, I was trying some octiamond game ideas with Adrienne Siskind, and she offhandedly suggested the set of rules above.  This simple game was a hit!  I've packaged it as six framed levels, plus two blanks above and below to form a box, held together with nuts, and machine screws.  The unit side is half an inch.
Each layer is cut from a different color of transparent acrylic, 1/8 inch thick.  With eight layers, the whole assembly is one inch thick.  All quite beautiful.  Here are two more pages I'm sending with the game, cut to the same size as the above picture.
  Here is one of Patrick Hamlyn's discoveries:
More Iamond material is at my Iamond page.  Here is a wonderful solution by Michael Dowle.

Here is a $50 contest for the octiamonds.  You don't have to buy my set -- you can make your own, or create them on a computer.

The Third Octiamond Contest -- Octiamond Solitaire
A piece that has no holes under it is said to be completely supported.  At every stage of the game, each piece must be completely supported.  Use the full set of 66 octiamonds, without reusing any.
Start:  Put one octiamond piece down.  This is level one.
Stage 2:  Add an octiamond to level one.  Put another octiamond on top, starting level two.
Stage 3:  Add an octiamond to level one, then add another to level two, then put another on top to make level three.
Stage 11:  Add an octiamond to level one, then add another to level two, then add another on level three, ..., then put the last octiamond on top to make level eleven.
Is this possible?  The first to send either an answer or an impossibility proof wins $50.
This was solved by Wei-Hwa Huang.  See http://www.mathpuzzle.com/prizes.html

Some more solutions by Michael Dowle:

You can try a solitaire version of Border Patrol. Here, you will find seven pieces.  Put one of them in the center.  Add pieces one at a time so that zero or fewer sides are added each turn.  In my solution, the number of sides added each turn is (0, -1, 0, 0, 0, -3).  Here are two triangles by Michael Dowle.

Here are some Octiamond puzzles by Michael Dowle
Can the octiamonds be packed in a different box?  Here's another way the octiamonds can pack (by MD).
Here are more problems.  Solutions are available for any of these shapes.

Here a a beautiful wreath pattern by Michael Dowle

Available at my orders page.  Andrew Clarke's solution for four side-19 triangles with holes at their center is below. This is the image I used to cut sets of enneiamonds.  I'm wondering if anyone can find five side-17 triangles with identical holes.  The iamonds seem to love making triangles.  The 24 heptiamonds can make a side-13 triangle with a hole in the center, and the 66 octiamonds can make a side-23 triangle with a hole at the center.   For more about the enneiamonds, Andrew's polyform website is here.  His solution is below.    To order them, see my Orders page.

An enneiamond solution by Andrew Clarke.
I've cut 8 sets of the 448 deciamonds.  See my Orders Page. Andrew Clarke calls them dekiamonds.  Brendan Owens sent me pictures of the 11-iamonds (hendeciamonds) and dodeciamonds.

I'm putting the Autocad files for the deciamonds into the public domain.  Here are Autocad files for ten1, ten2, and ten3.  Most cities can provide both plastic and laser cutting.  With the deciamonds, you and your family can make the lovely 12 foot strip of shapes below (By Patrick Hamlyn).