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 Post subject: The first puzzle I made in 1974
PostPosted: Wed May 21, 2008 11:04 am 
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Joined: Sun Nov 25, 2007 7:29 am
Location: UK
A recent topic http://twistypuzzles.com/forum/viewtopic.php?f=9&t=9784 reminded me of this.

I was sat around in 1974 waiting for someone to invent the Rubik's Cube when I read an article on hexaflexagons. I made a 6 surface one and the more difficult to make 12 sided version which I think was called a super hexaflexagon.
You have to expose all the surfaces by flexing and reopening it.
Image
I remade the smaller puzzle in black and white from memory today: http://www.youtube.com/watch?v=cRZLn_nmNxs

Here is a useful site if you want to make picture versions http://hexaflexagon.sourceforge.net/

I found this background.
"In 1939 while a graduate student at Princeton, Arthur Stone invented what is known as a hexaflexagon, a hexagonal flat figure folded out of a strip of equilateral triangles. This object can be flexed and rotated to bring different faces to view. At the time of their invention, the flexagons were an interesting mathematical recreation. They were also useful to topologists as an example of a Mobius strip, albeit an unusual one."

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 Post subject: Re: The first puzzle I made in 1974
PostPosted: Wed May 21, 2008 12:52 pm 
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Wow, those are really cool.


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 Post subject: Re: The first puzzle I made in 1974
PostPosted: Wed May 21, 2008 1:14 pm 
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I vaguely remember these from about the same time. I think my brother made one around then, or maybe a bit later. It came from a magasine called "Games and Puzzles".

I wander if that was your source too?
[Edit]
Closer examination reveals this wasn't your source! I will see if those old magasines are stored away somewhere....

They are an intriguing design both in the making and the flexing. Its funny I was thinking about these a couple of weeks ago when looking at a similar idea from a book made from several sheets of A4 made into rhombic solids. It is interesting to see them again!


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 Post subject: Re: The first puzzle I made in 1974
PostPosted: Wed May 21, 2008 11:24 pm 
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Uh, Gardner?
I need to fold me some again...

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 Post subject: Re: The first puzzle I made in 1974
PostPosted: Wed May 21, 2008 11:47 pm 
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I can't remember the exact source. I think it was a library book, possibly Martin Gardner. There was a lighthearted story of someone whose tie got caught up in the folds and was stuck inside the puzzle till someone else played with it.

All the current versions I've found are pictorial and some are very nice.

The 12 version (dodecahexaflexagon) was made from a strip twice as long but I'm having trouble recreating that one at the moment. I think you made a second helix from the first then folded into the hexagon. And I also remember that in some positions the alternate sectors were very thick and thin.

[edit]LOL I found those letters
Anyhow, the articles by Gardner in the Scientific American aroused many feelings, and he received hundreds of letters. These are two of them, published in the March and May issues in 1957.

SIRS:
I was quite taken with the article entitled "Flexagons" in your December issue. It took us only six or seven hours to paste the hexahexaflexagon together in the proper configuration. Since then it has been a source of continuing wonder. but we have a problem. This morning one of our fellows was sitting flexing the hexahexaflexagon idly when the tip of his necktie became caught in the folds. With each successive flex, more of his tie vanished into the flexagon. With the sixth flexing he disappeared entirely.
We have been flexing the thing madly, and can find no trace of him, but we have located a sixteenth configuration of the hexahexaflexagon.
Here is our question: Does his widow [draw] workmen's compensation for the duration of his absence, or can we have him declared legally dead immediately? We await your advice.

Neil Uptegrove

Allen B. Du Mont Laboratories, Inc.
Clifton, N.J.


SIRS:
The letter in the March issue of your magazine complainting of the disappearance of a fellow from the Allen B. Du Mont Laboratories "down" a hexahexaflexagon, has solved a mystery for us.
One day, while idly flexing our latest hexahexaflexagon, we were confounded to find that it was producing a strip of multicoloured material. Further flexing of the hexahexaflexagon finally disgorged a gum-chewing stranger.
Unfortunately he was in a weak state and, owing to an apparent loss of memory, unable to give any account of how he came to be with us. His health has now been restored on our national diet of porridge, haggis and whisky, and he has become quite a pet around the department, answering to the name of Eccles.
Our problem is, should we now return him and, if so, by what method? Unfortunately Eccles now cringes at the very sight of a hexahexaflexagon and absolutely refuses to "flex".

Robert M. Hill

The Royal Institute of Science and Technology
Glasgow, Scotland

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