Well, this is not a new puzzle, but it is a BRILLIANT one.

It was made by Markus Goetz a few years back, and it also won
an award at the design competition. It is based on ternary, not
binary, making it harder for those who are indecisive.



After finding the website with the java applet game, I ended up
with some nice laser cut pieces which I assembled. It works
really nice (although I made it a bit tight LOL).

The video which I made yesterday using one step down (to make things easier):
http://www.youtube.com/watch?v=52cTbD7v8FI

Information and java game here:
http://www.markus-goetz.de/puzzle/0019.html




Pantazis

I just solved the 5 elephant java applet, it is not a hard puzzle but it is fun. The hardest part is remembering how the elephants can turn as you can't actually see this.
It also just looks awesome

I was hoping this would be a bit harder. I haven't had any issues up to 4 so far, and I'm finding it very similar to the spinout.

We'll see if it gets a bit harder. It's a neat concept, but there's no reason to get into a dead end position when all the elephants start facing up.

Mmkay, it doesn't get harder, but it does get a bit more frustrating. I can't seem to hit one button at a time! >:(

Forgive my stupidity and lack of understanding. Did you buy this? Or make it?

I want one! It is so cute!

LOL I know it can be frustrating on the java applet,
which is why I wanted to get a physical copy.

The puzzle was made years ago by Markus Goetz,
and the laser cut pieces were sent to me from Europe
(Peter Knoppers) to finally assemble it.




Pantazis

AHA. No more multiple button hitting, the arrow keys work. How many elephants does it go up to? I should be on the scoreboard in a bit.

GAH! I didn't save the codes from each level, only level 6! Guess I have to do it again.

This is like my spin-out puzzle! That one was always one of my favorites. This is a little more interesting though.

going through some of his other things I saw the triagonal slide out. Try this one, it's pretty fun!

http://www.markus-goetz.de/puzzle/java/0021/crh.html OMG LEVEL 13!

I'm on the list for crazy elephant dance!

LOL well done being in the list!

And that level 13, such a synchronised movement.... nice!!!




Pantazis

For those who like sliding-block puzzles, here is an independent realization of the same idea in pure sliding-block form:

http://www.hearn.to/block-rings.pdf

Sorry, no applet! Like Crazy Elephant Dance, it's essentially a ternary version of the Chinese rings. The back story here is that this was not originally designed as a puzzle, as such, but came out of my proof that sliding-block puzzles in general are PSPACE-complete (essentially, a proof that there can be no efficient algorithm for solving sliding-block puzzles).

Thanks Bob, nice one!

There can really be plentiful nice puzzles using different mechanisms,
just based on simple number bases.




Pantazis

To the best of my knowledge, the Loony Loop Puzzle is the first known exhibiting a ternary Gray code solution (in a suitably generalized form). I think this was first discovered by Don Knuth -- at least, I heard it from him in a talk -- but I'm not positive. This fact is mentioned without reference in Winning Ways: http://tiny.cc/8mi3q

I'll take your word for it.

I won't take your word for it. When was it proved that P doesn't equal PSPACE?

You've got me there (thus, my qualification "essentially"). If P = PSPACE, then all sorts of things every computer scientist assumes are true, are not. Generally this would be considered much less likely than P = NP, which nobody expects is true. If you prefer, replace "essentially" with "assuming standard beliefs in complexity theory".

I half accept, but I'd say "maybe essentially".

Some of us hope but don't assume.

To me sometimes it seems like the axiom of choice, where it often seems to be true but it's equally capable of being false. Of course this is also an intuitive feeling without being assumed or considered essential, since it hasn't been proved that the proposition P = PSPACE is an independent axiom the way the axiom of choice has been.

Pantazis,

I saw this picture in my daily newspaper today and suddenly thought of The Crazy Elephant Dance

http://www.mirror.co.uk/news/top-storie ... -22567072/

Hmm... I saw this topic a few days ago, but because it's not a twisty puzzle, it's not my thing. However, after watching the video, it looks like a very interesting puzzle.

LOL Justin!!!!

I guess finding some real elephants to perform in a such a ternary way,
may not be out of the question after all!




Pantazis


PS. Norman, you seem to grasp the Turing notion in such a mathematical way, that
you must be mathematician + computer science expert or something... am I wrong?

I used to be ... sigh.

By the way for those who aren't, one of my previous postings needs a clarification. Where the axiom of choice usually seems to be true but is equally capable of being false (having been proved to be an independent axiom), the proposition P = PSPACE usually seems to be FALSE but is equally capable of being true (not yet having been proved one way or the other or neither).

At present the most important practical reason for hoping that P doesn't equal PSPACE and moreover that P doesn't equal NP is the hope that it will remain possible to make encryption systems that are hard to break. If someone finds P solutions for everything in NP then we can expect to find criminals impersonating us in Twisty Puzzles postings and other sites that are supposed to be secure.

Sorry, this really is off topic. Both subthreads of this discussion belong in non-twisty puzzles

Agreed and done! I also modified the main title to include some tips of the thread's actual content.




Pantazis

Well with that tweak, I don't feel guilty about continuing off topic! So...


Funny how calling something an "axiom" makes it seem not at all strange that it could be independent (otherwise it wouldn't need to be an axiom!), but calling something an "hypothesis" -- like the Continuum Hypothesis -- makes its independence much more mysterious.

I have to admit that, as someone who's written a book on complexity theory (and puzzles!), I've never really considered the possibility that P = NP or P = PSPACE could be formally independent. My intuition argues against it. I found this paper, which makes interesting reading (and ultimately also argues against the possibility):

http://www.scottaaronson.com/papers/pnp.pdf

Just found this thread. There are some other puzzles with binary, ternary and other n-ary scheme. A list of the ones I know can be found in this article:

http://www.schwandtner.info/publications/Kugellager.pdf

Very nice! But you are missing the Loony Loop (referenced above), perhaps the first puzzle with a ternary Gray code solution (when generalized). (Also my ternary sliding-block puzzle from 2004, but that was never publicized.)

Bob, thanks for noticing. I have updated my article with some references and links to your article and puzzle, also the Loony Loop. I wonder how I could miss it when I was reading the Winning Ways books.

I had a short look at your space complexity paper about the space complexity of sliding blocks puzzles. I like your way of building logical gates and circuits using sliding puzzles and it reminds me of some puzzle boxes I have seen, e.g.
http://www.kagenschaefer.com/Block2.html

I will have a look into your PhD thesis/book to find out more about the complexity of puzzle and I am looking forward to it. At university I never got around to publish some results e.g. on the NP-completeness of the Mahjongg solitaire game, where you remove pairs of equal Mahjongg stones, and my PhD thesis only involves complexity theory, but no puzzles ...

Before it looks like I am hijacking this thread, I'm going back to my n-ary puzzles ...

currently i'm the most recent to solve it