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 Post subject: More details on the Unscrambled and Turn Apart puzzles
PostPosted: Sun Jan 06, 2008 8:24 am 

Joined: Mon Oct 22, 2001 12:45 pm
On October 24th, two puzzles by Oskar van Deventer were presented at this forum ( viewtopic.php?t=8024 ); the Turn Apart puzzle and the Unscrambled Puzzle.
The latter puzzle is a co-invention with Bram Cohen.
Additional information on these puzzles was also given in the marketplace section of this forum: viewtopic.php?t=8025
and in various updates that were sent to the people who showed interest in these puzzles.

A number of these puzzles have been made in the meantime and as a result Noah also made some additional remarks: viewtopic.php?t=8573

Below is some additional information on these puzzles that was partly already sent via the above mentioned updates.
For additional pictures of the puzzles, I refer to the links given above.

The initial few samples of both puzzles were made by means of FDM by George Miller.
In simple words, FDM is a rapid prototyping technique which works a bit like applying ‘toothpaste’. Very thin layers are deposited, one on top of the other.
The new samples that are being made are made by means of SLS (Selective Laser Sintering).
This is also a layer-by-layer rapid prototyping technique which uses nylon powder as material. The nylon powder is preheated to just below the melting point and by scanning a laser a thin layer of material is ‘locally’ melted. The melted part is lowered in the machine, a new thin layer of nylon powder is spread out and next a new layer can be melted by means of the laser. Both rapid prototyping techniques may be used to make very complex products. A disadvantage of the techniques is that the thin layer structure remains somewhat visible. A disadvantage is also the restricted use of material. FDM may apply more materials and colours (including ABS), but SLS can only apply nylon which results in products which have a different feel than we are used to for twisty puzzles.

The tolerances on both puzzles need to be rather precise.
A careful compromise is needed for these puzzles to avoid that they are either too loose (wobbly) or have too much friction.

Puzzles made by means of SLS out of nylon tend to get a bit dirty.
However, the nylon can easily be coloured using textile dye (e.g. Jacquard Acid Dye,
This is powder, which added with vinegar acid and half an hour of ‘cooking’ will result in nice colours.
Dirty puzzles can also easily be cleaned in the dishwasher.

The Unscrambled puzzle:
The Unscrambled puzzle consists of 11 pieces; 7 pieces have an equal angular ‘width’ (32.7 degrees), two are wider (49.1 degrees, pieces ‘U’ and ‘B’) and two are smaller (16.4 degrees, pieces ‘C’ and ‘L’). The 7 pieces have a ‘knife’ side and a ‘groove’ side. The wider pieces have 2 ‘grooves’ and the smaller pieces have 2 ‘knives’.


There can be considered to be two puzzle objectives related to the Unscrambled puzzle:
1. Assembling the puzzle
2. Twisting the assembled puzzle and restoring it to the original start-position.

In order to assemble the puzzle, there are 4 pieces that contain small ‘notches’ at the inside and outside:
- left part of piece D (groove)
- left part of piece M (groove)
- right part of piece L (knife)
- left part of piece C (knife).



Assembly requires a set of 6 preassembled pieces and a set of 5 preassembled pieces such that the 4 pieces with the notches are at the outside.
By positioning these two sets 90 degrees with respect to each other, the two sets of pieces can be fitted together, after which a quarter turn will result in an assembled but not yet solved puzzle.

As mentioned above, the tolerances for both puzzles need to be rather precise.
Too tight tolerances for the Unscrambled puzzle mean that the puzzle cannot be rotated when it should be able to be rotated and too wide tolerances mean that the puzzle is too loose. This also means that too quick turning can result in additional pieces that are also moving, as well as in situations where the puzzle is becoming (almost) disassembled. This is the case in the situation described by Noah, which should be avoided in order not to damage the puzzle.
In case the puzzle is somewhat too loose, this can be avoided by careful turning and/or by holding the pieces of the puzzle a bit together (by applying some force from the outside). This requires some getting used to (it is also not a speedcubing puzzle).

Solving the puzzle requires that two halves of the puzzle are rotated with respect to each other a repeated number of times until the ‘cubic’ shape is created and the letters at the outside of the pieces will read ‘Unscrambled’. As explained by Bram Cohen, the puzzle can be regarded to be a kind of bandaged 22-piece puck, which has a clever parity restriction to allow the pieces to be all about the same size. Typically, at any given position there will only be 1, 2 or 3 ways in which the puzzles halves can be rotated.

The Unscrambled puzzle is practically impossible to solve by hand.
First of all, random assembly may result in an unsolvable puzzle and even when assembled correctly, it takes some 20 moves to arrive at the ‘Unscrambled’ position.
Listed below is a sequence that can be used to arrive from the Unscrambled state to the position at which the puzzle can be disassembled (after a 90 degree turn). It is intended to flip the pieces between the -'s; small (non-capital) letters indicate that the particular piece is ‘upside down’.

Step 0: UNS - CRAMBL - ED
Step 1: UNSlb - marcED
Step 2: UN - SlbdeC - RAM
Step 3: U - NcEDBL - sRAM
Step 4: Ulb - deCnsR - AM
Step 5: UlbrS - NcEDAM
Step 6: Ul - brSma - deCn
Step 7: UlA - MsRBd - eCn
Step 8: Ul - ADbrS - meCn
Step 9: UlsRB - dameCn
Step 10: U - lsRBNc - EMAD
Step 11: UCnb - rSLEMA - D
Step 12: UCnba - melsRD
Step 13: UCnb - adrSLE - M
Step 14: UCnbe - lsRDAM
Step 15: UC - nbema - drSL
Step 16: UCAME - BNdrS - L
Step 17: U - CAMEsR - DnbL
Step 18: UrSem - acDnbL
Step 19: UrSe - mlBNdC - A
Step 20: U - rSecDn - bLMA
Step 21: UNd - CEsRbL - MA

A full solution applet is available in the meantime which will be presented as soon as the puzzles which are currently being made have been sent.

The Turn Apart puzzle:
The Turn Apart puzzle has 8 pieces which each have 3 ‘tongues’ and/or ‘grooves’.
There are 4 different kinds of pieces:
-1x "female-female-female"
-2x "male-male-female"
-1x "male-female-female" type 1
-4x "male-female-female" type 2

Tongue and groove pieces that are interlinked can only be separated by turning.
For the 8 puzzle pieces there are 12 contact planes. There are 9 ‘tongues’, so only only 3 planes have no ‘tongues’ and can be separated without turning.

The basic idea behind the puzzle is as follows:
- assemble 6 pieces (this is the easy part)
- turn the pieces such that the 7th piece can be added
- turn the 7 assembled pieces such that the remaining open spot has only grooves visible, after which the 8th piece (the "female-female-female" piece) can be added
- turn the 8 pieces such that the rim at the outside becomes nicely aligned.

This may all appear relatively easy, but in fact is more difficult because certain movements are blocked (due to the shapes of the ‘tongues’).


 Post subject:
PostPosted: Sun Jan 06, 2008 1:03 pm 

Joined: Sun Mar 27, 2005 7:37 pm
Thanks for that information Geert.


 Post subject: Re: More details on the Unscrambled and Turn Apart puzzles
PostPosted: Sun Jan 06, 2008 1:37 pm 
User avatar

Joined: Sat Apr 22, 2000 2:51 am
Location: New Ulm, Minnesota, USA
Geert Hellings wrote:

A full solution applet is available in the meantime which will be presented as soon as the puzzles which are currently being made have been sent.

Is this on a website somewhere or downloaded your own computer or comes on a disk to buy later or is this to soon to ask?

Darren & Traiphum's Dual Helicoptrahedron
X-TownCuber wrote:
Are my eyes deceiving me, or is this the coolest puzzle ever?

 Post subject:
PostPosted: Sun Jan 06, 2008 6:41 pm 
User avatar

Joined: Sun Jun 04, 2006 10:05 am
Location: Minneapolis, Minnesota, USA
Yes, I've been turning the puzzle by applying slight pressure to keep the puzzle together. I'm still very fond of it. I even got to show it off to a random 13 year old speedcuber (he was playing with an ES5) today in the Minneapolis Airport.

Now, it was mentioned earlier that there was another version of the puzzle with a dihedral center similar to a regular puck. Did this improve the consistency of the tolerances?

And here is a question purely out of curiosity. If I were to take something, such as a glossy spray paint, and fully coat each piece with a thin layer, and after it dried, applied a layer of lubricant and reassembled it, would it be some what more stable? Right now I have no such plans to do such. This is just purely out of curiosity.

3x3 PB 22.63
3x3 Av 30.57

25, Male
Started cubing Oct 15 '05

Out of the game, but not completely.

 Post subject:
PostPosted: Mon Jan 07, 2008 12:51 am 

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
The version with two central pieces is quite a bit more robust and thoroughly prohibits 'cheating' even at the same tolerances, although it isn't quite as elegant as a puzzle.

Yes, if you coated it with an even layer of a strong coating it might work better, but the coating would have to be very even and very strong, and if you screw it up it could become too tight to turn.

 Post subject:
PostPosted: Mon Jan 07, 2008 1:03 am 
User avatar

Joined: Mon Sep 09, 2002 2:19 pm
Location: Yaroslavl, Russia and Maryland, USA
Are these [inexact] tolerances due to limitations of the [SLS] printing process or was it done this way deliberately? Also, it looks like with the FDM process the puzzle turned out better, then why was it replaced with SLS? Thanks!


 Post subject:
PostPosted: Mon Jan 07, 2008 11:25 am 

Joined: Sat Mar 22, 2003 9:11 am
Location: Marin, CA
The tolerance issues mostly have to do with the limitations of the printing process. Some gap was added intentionally to allow the pieces to slide smoothly, and it's possible that SLS could be done with a lower gap (I'll let everyone know my opinion when I get it) but mostly the issue is that this is a very demanding puzzle design to build, requiring very precise tolerances.

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