Hi Twisty Puzzles fans,

More Madness is a deeper cut version of Meteor Madness, both of which are based on the geometry of a Triangular Di-pyramid. Bram Cohen calls this strange type of shape shifting "jumbling". This geometry, discovered by Bram, is the simplest twisty-puzzle geometry that jumbles.

I have been playing with this puzzle for quite a while now. It's playing experience is very different from "regular" twisty puzzles. Shape-shifting is mandatory, as every move results in a different shape. The puzzle acts very bandaged. At first, I felt that the puzzle could not be scrambled. But once scrambled, it keeps changing shape, leaving me clueless how to get this puzzle back in shape, let alone how to get it solved. It is a bit like a maze. From many states you can go only two ways: forward and backward. There is an occasional junction. It is very easy to mis a junction and feel stuck,moving in circles. But it also has the same fun of a maze, suddenly discovering and exploring new aspects of the puzzle.

Watch the YouTube video.
Buy this puzzle from my Shapeways Shop.
Read more at the Shapeways Forum.
Check out the photos below.

Enjoy!

Oskar

I don't even really understand jumbling, this is just............wow.

Alex

I'm speechless.

Thomas

Agreed with APJ. I get what jumbling is, but the design and implementation process of that into a puzzle is beyond me. Fabulous work, Oskar.

Wow ...I'm completely messed up by this...


this is great work...i wanna see more like this from you oskar

I second that. Yes Oskar, we definitely want to see more like this. Wow, so simple yet so mischievous. Very very cool.

Kudos!

Skarabajo.

Wow! Complicated, confusing, everything you want in a puzzle!

At first I was like but then I was like

It seems a little large... I'm guessing the mechanism wouldn't work well if it were much smaller?

This is one of my favorite puzzles you've made. Are the pieces hollow?

-Eitan

Yes, as hollow as they can be. The wall thickness is 0.7 mm everywhere, Shapeways minimum. Moreover, I have punched many holes in the spherical core to reduce weight. This is why the price is so, ... eh, affordable for hopefully someone?

Oskar

.7! That is crazy! I went as low as .8, but I didn't think it was safe to go lower! That is insane!

Ah, ok. Perhaps at the end of the summer, if I've made enough from my job, I'll order one.

-π (Eitan)

I'm surprised by (a) how magical the motion of this thing looks, and (b) what a great response it's gotten. Apparently my ability to guess how cool puzzles will be still sucks.

The equivalent with the square antiprism geometry would *probably* be less bandaged-feeling. It might feel a bit more because it has so many pieces. It's hard to tell. These puzzles are very mysterious.

I have been playing with my More Madness puzzle for some time. I have returned it to its original shape twice, but I am still clueless how that works. Even two moves away, I cannot see that I am even close to its restored shape. The puzzle is seriously scrambled now, but at least back in shape.

The puzzle has some unexpected bandaging. Sometimes, a move looks possible at the outside, but it is blocked on a (hidden) center piece. This is a bit similar to the Nightmare Cube, which is internally bandaged.

In order to better understand the puzzle, I drew its Jaap's Sphere. As Jaap Scherphuis' applet does not support jumbling geometries, I used CAD to draw it. The attached 3D PDF allows you to turn the Jaap's Sphere and see it from other sides.

The red lines represent the outer cuts.

The green lines represent the inner cuts.

If you look carefully, you can see a red square on the left that corresponds with one of the three pointy ends, and a big green isoceles triangle on the right that corresponds to one of the six hidden turning centers.

I hope someone will make a full analysis of this puzzle some day.

Oskar

I'm working on it, believe me, but you have unlocked a whole new WORLD of twisty puzzles here, Oskar. I'll give more details later when I'm more comfortable with them on exactly what I've been researching for the past two months but let me say this: finding a pattern between Asteroid Attack, Meteor Madness, and Fairly Twisted, I have compiled a list of possible puzzle constructions that amounts to well over 3000 new, never-before-seen puzzles and includes seven instances where a particular setup can be augmented infinitely, producing in theory an infinite list of theoretically possible puzzle designs. I'm not going to comment on how possible it is to physically construct any of these because frankly I dont know I have so far tested 2 particular puzzle designs in this list at random. One seemed entirely possible. The other one was a physical anomaly and cannot be physically produced. Go figure.

Anywho, the SIMPLEST of all these puzzles is basically the Meteor Madness, or technically a Meteor Madness "bandaged" in a particular way. The only cuts in this simplest puzzle are those that initially lie* in the 6 rotation planes, reducing the total number of visible pieces to 17. Since I did purchase Oskar's Meteor Madness puzzle, I have simulated this "default" puzzle on it and found a very similair "maze-like" phenomenon happening. With so many moves blocked so often, you very rarely have a choice and the puzzle seems like wandering through a maze that somehow systematically rearranges itself with every move. I felt so trapped by the so frequently blocked moves that I didn't even know where to begin to solve it

However, I compared this to the current design of the Meteor Madness, where additional cuts are made, breaking up many of the bandaged sections and freeing many of the once blocked moves. Oskar's choices on where to cut up these bandages have produced a puzzle with a neat rule. Namely: A move is blocked if and only if it is blocked by a center piece. Note this doesn't imply there aren't also other pieces blocking a move, but it does imply that if a center does not block a move, then there is guaranteed to be a clean cut through the puzzle allowing that move.

This makes getting the puzzle back in shape TRIVIAL. It's as easy as picking a center that is not blocked and rotating it to the right position, repeat x6. That's it. A trained monkey could get the puzzle back in shape in 3 seconds from any position. This allows the puzzle solver (me!) to organize a solving method and actually implement algorithms that can be used on multiple parts of the puzzle. The jumbling remains but the puzzle no longer FEELS bandaged. And yes many moves are still blocked as the puzzle changes shape, but it is much more predictable. You're no longer wandering around the "maze", blinded by so many blocked moves that you are rendered helpless at trying to accomplish anything. Instead you are faced with a puzzle that in many ways acts like a rubik's cube, but one that has been somehow warped throught an alternate dimension and seems to implement illegal geometry. It's really much more fun!

Anyway the point I was going to make is that the Meteor Madness puzzle has the extra cuts that free it from the bandaged feeling, while the More Madness puzzle lacks these freedom cuts. The bad news is that I believe every single one of the puzzles on my list will run into this problem of blocked move harassment. The good news is I believe every one of them can be "freed" by adding the extra cuts. Unfortunately these extra cuts don't always come out as pretty as they have on the Meteor Madness, Asteroid Attack, or Fairly Twisted puzzle, where it always seems to cut the edges into near perfect thirds....

I haven't looked into this enough yet, but I can present you with a quick CAD drawing. I believe the rotated face in the picture below has the correct "freedom cuts" though I can't be sure. This is by far the most complicated geometry I have ever messed with and it has been producing some STRANGE coincidences.
(for example the cuts along any edge of the More Madness puzzle lie on intervals that divide the edge EXACTLY into sevenths... This puzzle's geometry is built from triangles and squares, it has 6 turning faces, and 26 pieces of 5 different types. Where the hell did the 7 come from?????????)

I will be sure to let the forum know if I make any breakthroughs on this COMPLICATED subject

Peace,
Matt Galla

P.S. Thank you Oskar very much for the Meteor Madness puzzle. I have fully scrambled and solved it 3 times now. Every assemble-able position IS reachable with the usual restrictions that there must be an even number of swaps among both edges and "corners" and neither a single edge may be flipped nor a single corner rotated 1/3. However the interactions are very complicated and you often must get the puzzle out of shape in order to really manipulate things, leading to very long, tricky setup sequnces and a couple of clever maneuvers. The puzzle was the PERFECT challenge for me at my current skill (which I like to think is quite good ). Quite difficult, not repetitive at all, and the perfect number of pieces to keep it interesting but not overwhelming. I plan to make a more in depth review sometime in the near future

*it is generally well-known that twisty puzzle cuts in fact always tell the truth, except in the case of extended chinese knockoff cuboids

Matt,

I am happy that your Meteor Madness has arrived safely. Thank you again for your order and your nice words about my work.

You initial analysis looks interesting. I never realized that I had "freedom-unbandaged" pieces in Meteor Madness.

As for More Madness, I noticed some more funny aspects.

-More Madness has "overhang bandaging". If you look at the first picture, you see a pointy piece overhanging and blocking an otherwise viable turn.

-The twelve pieces that hold the three pointy pieces are internally asymmetrical if you build them from basic cuts. There would be six left-handed ones and six right-handed, see the second picture. This results in some sort of "internal bandaging", as it impedes moves that would otherwise be possible.

-Without realizing it, I have "freedom unbandaged" those twelve pieces by making them symmetrical and identical to each other, see third picture.

-A Nightmare Cube type of hidden bandaging remains, as the big hidden centers can block viable-looking moves some times. I assume it would be possible to unbandage the six hidden turning centers.

As Bram Cohen can tell you, it is impossible to fully unbandage a jumbling puzzle. You will chop the puzzle to dust while trying. I guess there will be more to explore about this puzzle ...

Oskar

Wow! This begs the following questions...

(1) Does this puzzle have any moves that AREN'T considered jumbling?
(2) If this is "deeper" cut, what does the deep cut version look like?
(3) Is it even possible to make a deep cut puzzle based on this geometry?

Carl

It looks like we are trying to establish a twisty-puzzles dictionary. While here is a discussion on the definition of jumbling, I haven't seen a proper definition on deep cutting yet ...

Oskar

My definition for deep cut is something like:
A puzzle in which the cutting plane divides the puzzle in half from the direction of the twisting origin

Where a twisting origin is such as a face (for a 2x2x2), edge (24 cube) or vertex (skewb).

So, what does that mean for More Madness?

I know its a bit old, but this thread discusses Cut Depth at length. I particularly like Cut Numbers as suggested by Pantazis and refined by DLitwin.

Edit: Fixed Link

I don't see the link you tried to post. Is this it?

http://twistypuzzles.com/forum/viewtopic.php?f=1&t=11001



Check out the link above. I think "deep cut" is pretty well defined for planar cut puzzles. For non-planar I'm not sure. Part of me still wants to call the Slice Kilominx a deep cut puzzle made with conical cuts that cut the puzzle into two isomorphic groups and all the cut surfaces intersect at a point (the center of the puzzle).

At least for planar cut puzzles if all the cut surfaces intersect at a point and each divides the puzzle into two isomorphic groups then the puzzle is considered deep cut.



Great question! Do all it's cut planes intersect at a point? During a rotation do you have the same number of total pieces on both sides? It may already be deep cut. I just can't tell from the pictures.

Carl

looking at the pictures, I think it's impossible to make a fully deep cut face-turning triangular dipyramid

The core of the puzzle looks to be a sphere. So if the cut planes are moved to the point they cut this sphere in half what happens?

Carl

I would not of thought of that I guess all puzzles can be deep cut now.

but, it doesn't matter if they cut the sphere in half, because the sphere doesn't appear to be at the center of the puzzle...
wait, that wouldn't make sense would it...

To be more precise, look at this posting:
viewtopic.php?p=181881#p181881

No. the cut planes miss the origin by just a couple of milimeters. No. There are 12 visible pieces at one side, and 14 at the other side.This is what such would look like. All cut planes go through the origin now. I do not know whether it can be actually constructed. Moreover, it looks even more bandaged than More Madness.

Oskar

If there was ever a Nobel Prize awarded for puzzle design...

I received my More Madness a few days ago. I stickered it, and made a video review.

http://www.youtube.com/watch?v=yqlXnEPBM8A

I absolutely love this puzzle. I hope to be able to get more of your puzzles in the future, Oskar. Is there any chance you could go through some of your old puzzles, and hollow them out? I'm talking about ones like Fairly Twisted, Crazy Comet, and the like, which cost over $300.

Thanks!

-π (Eitan)

Sorry for the slight bump but something about this puzzle has been bugging me and i had forgotten to mention it until now. It's about how many positions this could have. I don't think there would really be that many in comparison to say a 3x3x3 but i see no practical way of figuring that out. Has anyone figured out a way to find that out for any jumbling puzzle such as the helicopter cube? Is this also true for the more madness? i doubt it because it lacks the "freedom unbandaging cuts" but i could be wrong.

The only jumbling puzzles i have solved are the 6.2.1 spheres on gelatinbrain (though i have a helicopter cube in the mail) and the bandaging on them seems to pale in comparison to this crazy puzzle. I really feel this would be one of the most interesting puzzles to solve and even before i have tried i'd say it is one of my favourite twisty puzzles ever. I hope one day to be able to afford it but until then i will just have to admire the pictures and think about the discussion in this thread.