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Author Topic: 20 Ball Pyramid - How many versions are there?
James Sanford
Multiple
Member # 775

posted June 28, 2010 11:23 AM     Profile for James Sanford   Author's Homepage   Email James Sanford     Send New Private Message   Edit/Delete Post   Reply With Quote
As I mentioned in a previous thread, I am looking for a solution to one variation of the 20 ball pyramid puzzle which has 10 pairs of balls of different color combinations.

Since these balls are readily available and fairly easy to work with, I wonder how many variations of this puzzle are there. I am making these for grandchildren and neighborhood children.

One of the simplest has 6 pieces - two are 1x4 balls and four are 1x3 balls. Another common version is similar but has only 4 pieces - two are 1x4 balls and two are 2x3 balls. All are either parallel or right angle joints.

How many other variations are there? I have found some that are not easy to describe because the balls are joined at 60 degree angles.

I would appreciate any comments about ones you have found. Some of these puzzles are quite difficult to solve.

Thanks for the help.


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George Bell
Multiple
Member # 944

posted June 28, 2010 12:46 PM     Profile for George Bell   Author's Homepage   Email George Bell     Send New Private Message   Edit/Delete Post   Reply With Quote
I'm not familiar with the puzzle you refer to. But I would suggest using Burr Tools to analyze such puzzles. It can find all solutions to the puzzle given the pieces. You can even do color constraints, although I don't think they are of the "touching" type that you need. Regardless, you can find all solutions and remove those that don't adhere to your color rules (tedious, but possible).

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http://home.comcast.net/~gibell


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John Dawson
Multiple
Member # 1737

posted July 02, 2010 07:52 PM     Profile for John Dawson   Author's Homepage   Email John Dawson     Send New Private Message   Edit/Delete Post   Reply With Quote
Here's something that may help:

<http://www.dealtime.com/xPO-Channel-Craft-Oops-Again-Natural-Puzzle>


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John Dawson
Multiple
Member # 1737

posted July 02, 2010 07:58 PM     Profile for John Dawson   Author's Homepage   Email John Dawson     Send New Private Message   Edit/Delete Post   Reply With Quote
Maybe this is better. Amazon is always better.
http://www.amazon.com/Channel-Craft-Again-Natural-Puzzle/dp/B000BXFM04

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James Sanford
Multiple
Member # 775

posted July 20, 2010 03:04 PM     Profile for James Sanford   Author's Homepage   Email James Sanford     Send New Private Message   Edit/Delete Post   Reply With Quote
My objective in asking this question was to be able to make as many variations as I could. The round balls and dowels are readily available. I have a nephew who is interested in puzzles and I would like to continue to challenge him.

Here is what I have found so far:

1. The first and possibly the easiest to solve has six pieces - 2 pieces @ 1x4 and 4 pieces @ 1x3. One source is Pentangle Puzzles. Their name is Ball Pyramid (PP-BPX) and Pyramania 1 (PY-01) http://www.pentangle-puzzles.co.uk

2. The second version has four pieces - 2 @ 1x4 and 2 @ 2x3. This was the first version I encountered. Rob’s Puzzle Page states “Tut's Tomb by Mag-Nif is a 4-piece classic”.

3. Another variation from Pentangle Puzzles Pyramania 2 has 16 red balls and 4 white balls arranged – 1 @ 1x4, 2 @ 1x2, and 4 @ 1x3. One solution of this puzzle is to arrange the pyramid with one white ball on each face.

4. This same configuration 1 @ 1x4, 2 @ 1x2, and 4 @ 1x3 has been sold with either 4 balls each of 5 colors or 5 different woods. The objective of these puzzles is to stack them so that no two of the same color or wood type touch each other on any row or diagonal of any of the faces. These are produced as Pyramania 3 by Pentangle and OOPs Again by Channel Craft.

5. A variation called OOPS made by Channel Craft has 10 pairs of colored balls, 4 each of 5 colors. They also have made a version which used 5 different types of wood. The objective is to arrange the pairs of balls so that no two colors or wood types touch each other on the faces of the pyramid.

6. The Interlocking 20-Ball Tetrahedron is a relatively new puzzle by George Bell. This puzzle has two identical pieces of 5 balls each with two mirror image pieces. The beauty of this puzzle is that it locks together and does not require a base to make it easier to assemble. Without the clue that George provides on his website, this puzzle may still be in pieces. http://www.shapeways.com/model/53633/interlocking_tetrahedron.html It may have been called Stan’s Tetrahedron previously.

7. The Perplexing Pyramid by the Gordan Bros. has six different-shaped pieces. The description on the Kadon Enterprises website is “This is the hardest of the size-4 pyramids around. Six crystal-clear pieces have a unique solution to form an order-4 tetrahedron..” http://www.gamepuzzles.com/pyrpcs.htm

8. A 35-ball variation named the Giant Pyramid by the Gordan Bros. has nine pieces. Kadon states that there is “only one way to make the order-5 tetrahedron”.

9. The Lost Game of the Pharoahs is shown on Rob’s Puzzle Page as “a simple six-piece ball pyramid. 2 @ 1x6, 2 @ 2x5, 2 @ 3x4.” I don’t have this one so I don’t know how simple it is.

10. Another 4-piece puzzle called "Der Fluch des Pharao" (Curse of the Pharaoh) by Markus Goetz, made by Philos can be purchased from Funagain Games. The pieces apparently do interlock. I have not seen this puzzle so I am only restating what I have read other places.

11. Piet Hein's Pyramystery includes 6 pieces in different configurations which can assemble into a 20-ball pyramid, two separate 10-ball pyramids and numerous other shapes. When asked about the history or this puzzle, Mr. Hein also invented a history for this puzzle. One site states that this was the first 20 ball tetrahedron, pyramid puzzle. It is currently sold by Brilliant Puzzles. http://stores.brilliantpuzzles.com/catalog/Pyramid_Ball_New.jpg

Please let me know other variations that you have found. Thanks.


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George Bell
Multiple
Member # 944

posted July 21, 2010 01:15 AM     Profile for George Bell   Author's Homepage   Email George Bell     Send New Private Message   Edit/Delete Post   Reply With Quote
There is a nice booklet written around 1996 by Bernhard Wiezorke called "Compendium of Polysphere Puzzles". It lists about 50 ball puzzles, including Tut's Tomb, Stan's Tetrahedron, Pyramistery, and others that you have mentioned. He does not list any problems involving colors.

Sadly, the booklet is really hard to find. I managed to email Mr. Wiezorke last year, he told me he does not have any copies available. A friend happened to have two copies, though, so I finally got a hold of one.

Stan's Tetrahedron is not the same as my Interlocking Tetrahedron, although both designs interlock. I also wrote an article on polysphere puzzles which appeared in Cubism For Fun #81 (March 2010). You can google that name to read about that publication. If you send me your email address I can send you a pdf copy of my article.

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http://home.comcast.net/~gibell


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