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 Post subject: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 12:19 am 
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Sometimes people ask me which bandaged cube they should get. I tell them to get the cubetwist diy kit. I've written about it here and I still think it's an amazing kit. But having the kit doesn't solve the problem of "which bandaged cubes should I make, and in what order?" Someone new to the kit can easily make a bandaged puzzle with, say, one 2x1 block in an edge-corner position. It's a good intro to bandaged puzzles, but it won't be too taxing. What next? a puzzle with two 2x1 blocks, or a puzzle with one 3x1 block? Perhaps a 2x1 block in a center-edge position, rather than an edge-corner position? Obviously, the positioning of blocks can be as much part of the difficulty as the actual blocks.

So here's my question to anyone who has an opinion on it:

Is there is a logical progression in difficulty from the easiest bandaged variant to the hardest bandaged variant? If so, what is it?

Andreas said somewhere there were around 4,000 makeable puzzles from that kit. Obviously I'm not after a list in order of all 4,000. But it would be great to know some general ideas and thoughts about such a progression.

As an example, I can solve 4 of the 5 mass-produced bandaged 3x3 puzzles, but not the bicube. I'm sure there are lots of bandaged puzzles in between the ones I can solve and the ones I can't. But I'd much rather have some kind of logical thought process about it than just randomly stick bandaged blocks on and hope I produce the ideal puzzle.

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 1:43 am 
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I know what you mean Rline,

I like to solve things in some sort of order otherwise you get people saying "the (Flibberdy gah) puzzle? Oh yeah that one is easy its just like solving a (Oojy-mah-flip) puzzle with a slight difference". But you didnt know you should have attempted (Oojy-mah-flip) first in order to learn (Flibberdy gah).

But saying that, I don't think there is a natural progression. Just Burgos "beginners, intermediate, hard & very hard" categories.

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 4:12 am 
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My difficulty levels in the Bandaged Cube thread are based on a specific criteria, which I've stated there. In reality it's the same as other solving.. It's a bit subjective as to what, in particular, different people will find difficult. It depends on their approach, and if they get caught on something they haven't come across before. In most cases, I'd say it probably doesn't matter past a general idea.

For me, there's more a type of bandaged puzzle that I 'enjoy' solving.

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 7:43 am 
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What I've found that makes a bandaged cube difficult is if there are a lot of unbandaged pieces, yet the bandaging that is done makes the puzzle very restricted. This would mean more pieces to solve (as they are not bandaged) but would make it hard to solve them. So the hardest bandaged cube has the least number of bandaged pieces bandaged in such a way that the puzzle becomes the most restricted as possible. The bandaging doesn't even have to involve actual pieces. TomZ's 90 constrained cube comes to mind.

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 7:55 am 
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benpuzzles wrote:
So the hardest bandaged cube has the least number of bandaged pieces bandaged in such a way that the puzzle becomes the most restricted as possible. The bandaging doesn't even have to involve actual pieces.

This is a great starting point. Thanks for contributing! Looking forward to the thoughts of others.

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 1:12 pm 
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rline wrote:
benpuzzles wrote:
So the hardest bandaged cube has the least number of bandaged pieces bandaged in such a way that the puzzle becomes the most restricted as possible. The bandaging doesn't even have to involve actual pieces.

This is a great starting point. Thanks for contributing! Looking forward to the thoughts of others.


I do not agree with this!
please try to solve BiNCube 5*5 (only one 1*1*1 cubic) and try Minotaur Cube 5*5 (many-many 1*1*1 cubic)...
but both of these puzzles are very-very-very hard !!!

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 1:16 pm 
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I build a many of Bandaged Cubes ... the most difficult is the hybrid cubes! please try my latest hybrid cube:
chimera shift from 8 diferent puzzles: std 3*3*3 и 4*4*4, Burr Cube, Fence Cube, Meson Cube, Spiral Cube, BiNCube, Monotaur cube!
good luck :)

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Fri Apr 25, 2014 7:02 pm 
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Hello

I ordered the 3x3 bandaged Kit some month ago and I want slowly increase the difficulty.
I think it should be not the goal to find an objective way to categorize the difficulty of a puzzle.
Maybe you could find a way to do it, but in the end it may be not meaningful for a human beeing.

For example: A good chess program will never miss a forced win in 4 moves - because it simply calculates all possible moves within this depth.
A human beeing would see the winning move in some positions immediately - in other positions even grandmasters need long time to find this move. That is because human beeings thinking in categories - they comparing things or positions to positions they already know. If the position matches with the experience they find the right move in one second. So I guess somthing is less obvious the more it differs from your familiar solving strategies.

So I think more significant for the categorization of the difficulty are the challenges of the individual solving strategy.

I.e. If I am reducing a 4x4x4 cube into a 2x2x2 using the same strategies like solving the 4x4x4 Ai bandaged cube it feels much harder than reducing it into a 3x3x3 cube and solving it then as a rubiks cube.
Why is this like that? Is it really harder?
For me - it is.
Essentially I would suggest at least 4 factors which may be relevant for the "feel of difficulty" or what makes a puzzle difficult for a human beeing.

1. The quantity of solving strategies you need for the particular solving method.
(i.e. for the ulimate method to solve a standard 3x3x3 cube you use 2 basic strategies (1. solving edges, 2. solving corners)
2. The maximum number of affordable set-up moves (for bandaged puzzles this point may become very complex)
3. The complexity of the commutators (for 3x3x3: eps 4moves, cps 8 moves)
4. How hard is it to keep the perspective (relevant for shape shifting puzzles)

Maybe there are more factors. Feel free to add some :-)

The next step could be to transfer the results of all factors into a number which is representative for the difficulty.
If such a number should make any sense it is mandatory to define a reference number.

As "nearly" anybody here can solve a 3x3x3 cube it looks obvious to define this as our reference puzzle.

Just an idea.

What do you think?

Cheers - Dr. Twist


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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Sun Apr 27, 2014 2:25 am 
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benpuzzles wrote:
What I've found that makes a bandaged cube difficult is if there are a lot of unbandaged pieces, yet the bandaging that is done makes the puzzle very restricted. This would mean more pieces to solve (as they are not bandaged) but would make it hard to solve them. So the hardest bandaged cube has the least number of bandaged pieces bandaged in such a way that the puzzle becomes the most restricted as possible.
I second this. This speaks in favor of the "3 Quads + 3 Stripes Cube".

Everytime I read something about the difficulty of a bandaged 3x3x3 I fall back in this track:
This deals a lot with your pre-knowledge. Years ago a member said: "Siamese 1x1x3 poses no new challenge because I already had all the algorithms I needed."
Starting with this statement I started a project to find "useless variants with respect to solving".
My goal was to find all bandaged 3x3x3 you have to learn to solve to come up with a set of sufficient algorithms. These algorithms should allow you to solve alle other variants.
Example: If you can solve the Siamese2x2x3 than you can solve the Siamese1x1x3. Not necessarily (mathematically spoken) the other way.
Three years ago the museum changed me priorities and I freezed that project.

Andreas


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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Tue Apr 29, 2014 2:56 am 
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First, thanks to those who have contributed so far, especially Dr Twist. I was hoping for more, but I guess it is what it is.

doctor twist wrote:
I think it should be not the goal to find an objective way to categorize the difficulty of a puzzle.
Maybe you could find a way to do it, but in the end it may be not meaningful for a human beeing.

I just can't accept this. :) Being a mathematics teacher, and having a love of patterns and order (yes, including the order of chaos), I think there must be some way to come to a reasonably sensible idea about some new bandaged variant.
doctor twist wrote:
Essentially I would suggest at least 4 factors which may be relevant for the "feel of difficulty" or what makes a puzzle difficult for a human beeing.

Good. This is a nice starting point.

doctor twist wrote:
2. The maximum number of affordable set-up moves (for bandaged puzzles this point may become very complex)

Could you explain more what you mean by this?

doctor twist wrote:
The next step could be to transfer the results of all factors into a number which is representative for the difficulty.
If such a number should make any sense it is mandatory to define a reference number.

Agreed, and agreed.

grigr wrote:
I build a many of Bandaged Cubes ... the most difficult is the hybrid cubes! please try my latest hybrid cube:

For myself, I'm having enough trouble thinking about the 3x3 versions, so I think I'll stick to them for now! I also tend to think that restricting this discussion to only 3x3 cubes makes it much more accessible, since many people have the 3x3 kit.

In thinking about it now, I'd like to throw some puzzles in here and have people "rate" them for difficulty. This would be very helpful, first to see whether my own "difficulty rankings" equate with others, and second, to try and come up with more objective criteria. I'm choosing the 6 bandaged puzzles which have been mass-produced by cubetwist. If you've solved or attempted any of these, and would like to contribute, please give them your difficulty rating between 1 and 10, 1 being super-simple (basically as simple as a 3x3) and 10 being impossible. If you want, feel free to give a reason or two for each one. I'll give my own ratings later.

Bicube http://www.hknowstore.com/locale/en-US/ ... 054d622571
Bandaged 3 http://www.hknowstore.com/locale/en-US/ ... 5f21580da3
Fuse Cube http://www.hknowstore.com/locale/en-US/ ... 7884911a2b
3-Slices http://www.hknowstore.com/locale/en-US/ ... 9c82a864c5
2-Bar 4 http://www.hknowstore.com/locale/en-US/ ... 06b4341c8d
Big Block http://www.hknowstore.com/locale/en-US/ ... 6b02ab4801

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Tue Apr 29, 2014 5:24 pm 
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Hello

I also hoped for more contribution on this interesting topic. I think bandaged cubes have so much potential and there is so much more to explore!
As rline said just the 3x3x3 bandage kit offers so many possibilities (maybe more challenges then all other mass produced puzzles together).
Now we (the puzzle community) got so many higher order cubes available - just try to imagine how much potential are in those cubes if we start to bandage them in sophisticated ways. (Just think how much fun the AI 4x4x4 bandaged cube was and how many new solving strategies were used)
But rline is right (in my opinion) - we should start with the 3x3x3 and try to develope some basic knowledge on the "art of bandaging" and on solving strategies first.

rline wrote:
doctor twist wrote:
I think it should be not the goal to find an objective way to categorize the difficulty of a puzzle.
Maybe you could find a way to do it, but in the end it may be not meaningful for a human beeing.

I just can't accept this. :)



ok - good luck :)

rline wrote:
doctor twist wrote:
2. The maximum number of affordable set-up moves (for bandaged puzzles this point may become very complex)

Could you explain more what you mean by this?


Ok - I will try

My initial point was based on kind of a "general solving strategy" of this form:

1. Set up pieces that the commutator can applied to get the desired result
2. Apply commutator
3. Undo setup moves

Basically this is the main solving strategy you use in most of your tutorials, right?
I.e. I never needed more than 4 setup moves (depends on the way you count moves) at the endgame on a regular 3x3x3 cube.
For Eitans star I wrote down some setups - because they were too complex or too long (for me) to memorize.
When I tried to solve the Hidetoshi cube I needed - because of the bandaging - much more moves to set up the pieces in the desired position as on a regular 3x3x3. So it felt more difficult (maybe if I solve it 100 times it will feel much easier).
I assume that if bandaging gets more complex and/or cause more restrictions then also the set up will take more and more moves and getting more complex.With complexity I mean, that everything becoming more interlaced. For example: You want to do a certain set up move, but you cant, because you are restricted due to bandaging. So you need another setup move to make the first setup move possible, and so on...

I hope that I was able to make clear what I mean. (It is not easy for me, because my english is not the best - I hope it is not too bad :-) )

--------------------------------

My difficulty ratings:

3x3x3 cube: 1 (reference)
Fused cube: 2 (used the same strategies like on the siamese mirror cube - piece of cake ;-) )
Hidetoshi cube: 4 (one new solving strategy was affordable - sort of fancy setups, not easy to find)


Btw: I´m keen on seeing more tutorials of you about 3x3x3 bandaged cubes (i.e. 3 quads 3 stripes, spiral cube)

Happy puzzling
Doc Twist


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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Tue Apr 29, 2014 11:42 pm 
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rline wrote:
In thinking about it now, I'd like to throw some puzzles in here and have people "rate" them for difficulty. This would be very helpful, first to see whether my own "difficulty rankings" equate with others, and second, to try and come up with more objective criteria. I'm choosing the 6 bandaged puzzles which have been mass-produced by cubetwist. If you've solved or attempted any of these, and would like to contribute, please give them your difficulty rating between 1 and 10, 1 being super-simple (basically as simple as a 3x3) and 10 being impossible. If you want, feel free to give a reason or two for each one. I'll give my own ratings later.

Bicube http://www.hknowstore.com/locale/en-US/ ... 054d622571
Bandaged 3 http://www.hknowstore.com/locale/en-US/ ... 5f21580da3
Fuse Cube http://www.hknowstore.com/locale/en-US/ ... 7884911a2b
3-Slices http://www.hknowstore.com/locale/en-US/ ... 9c82a864c5
2-Bar 4 http://www.hknowstore.com/locale/en-US/ ... 06b4341c8d
Big Block http://www.hknowstore.com/locale/en-US/ ... 6b02ab4801


Fused Cube: 1
Big Block: 3
3-Slices: 4
2-Bar 4: 6
Bandaged 3: 6
Bicube: 8
I reserved the 10 for the "3 Quads and 3 Stripes"


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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Wed Apr 30, 2014 3:15 am 
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Hi Rline,

I took a quote from the first post in the bandaged cube thread. Within it are my difficulty ratings of those and other puzzles. The order of the puzzles `within the categories` also reflects my opinion of difficulty progression. Note that I have left the Bicube as only `Difficult`, similar to Andreas. There are `harder` and more `exciting` puzzles and challenges IMO, but the Bicube is a `type` that some will find harder than others.. essentially `that type` are able to be `mapped` relatively easily (unlike other puzzles), it just depends if you have the tenacity to map them (a computer would do a better job). Incidentally, Evgeniy's Snake Cube is exactly the same difficulty as the Bicube IMO, I solved it not long ago.

I've been a bit slack in keeping it up to date lately due to some other certain commitments, but I think it's still a really good start in outlining difficulties for people `starting out`.

from the bandaged cube thread wrote:
The difficulty rating is my own only and I am trying to use a criteria rather than subjectivity alone. I’m presuming that most people will find things `a bit harder` when they have to diverge from how they would normally use sequences or use small setups, and `difficult` when you have to strategize, invent sequences, think ahead or use larger setups. It’s just for a bit of a guide for people starting out in the thread so they don’t have to tackle the most difficult puzzles before they are ready and become frustrated, so an approximate difficulty is good enough.

The list will also act as a bit of a record of the puzzles in the thread as a quick reference.

Quite Easy:
3 Slices, Fuse Cube, Big Block, 1x1x3 Block, 2 Bar, Edge Road, Corner Road

A bit harder (use known sequences creatively):
Belt Road, Stalactites, Unbandaged Big Block, Stalagmites and Stalactites (this is not too hard, just unorthodox), Detiled Corners Only Fuse-3, Bandaged Clock Planets other than Jupiter (are quite easy<>a bit harder depending on No of bandaged faces, Uranus might make it into mid range), 3 Bar, 3 Bar Clock, Mr T, Unbandaged Wall-i, Wall-i, Bandaged Loop, Unbandaged Flying Carpets

Mid-range:
Big Block Clock, Bandaged 3, Bandaged 3+, Unbandaged Big Block Clock, Stonehenge

Difficult (have to come up with a strategy and sequences):
Unbandaged YZ, Bandaged YZ, Fuse-3, Bandaged Fortress, Pendulum, Bicube, Snake Cube, Cross Road, Double Block

Very Hard:
Bandaged Clock Jupiter, Alcatraz, Double Block Clock, Flying Carpets
Cheers,
Burgo.

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 Post subject: Re: Bandaged puzzles difficulty progression
PostPosted: Tue May 06, 2014 8:14 am 
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Hey again,

thinking about measuring the difficulty of puzzles is -from my perspective- a very interesting topic.
Lately I surfed on the puzzlemaster website. The difficulty of puzzles on this site is rated from 1 to 10.
I guess they use a "mathematical" method to rate the puzzles. From a human point of view those ratings are kind of incomprehensible.

I give you an example:

The 3x3x4 is rated with 8
The 3x3x6 is rated with 10
P. Octo Star is rated with10

For a human being this seems not logic, or?
I know if I can solve a 3x3x4 then I can solve a 3x3x6 too. It is exactly the same, no new strategies just two layers more.
The Pitcher Octo star is much harder to solve than the 3x3x6 (in my eyes).

I would like to encourage you to check this site and compare the puzzle ratings there with your own experience.
Then try to think what it is, that makes a puzzle hard or easy for you.
I hope together we will find a more sensitive and more comprehensible method how to measure the difficulty of puzzles.

Please contribute :-)

Doc Twist


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