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 Post subject: On general approach to solvingPosted: Thu Sep 20, 2012 12:23 pm

Joined: Thu Jul 26, 2012 5:17 am
Several questions for experienced solvers, if possible:

1. When you get the new puzzle do you twist it from solved state and back in order to understand how pieces move and find proper algorithms and then scramble and solve or you scramble it immediately?

2. When exploring how pieces move from scrambled state do you need to make records in order to understand which pieces moved and which did not or you can keep all the state in memory?

3. When puzzle contains many identical pieces do you use something to differentiate one from another and understand which of them exactly are moving (like pieces of plaster)?

4. How you find algorithms? Just trying several commutators learning what they do and then trying to combine with setup moves and each other in order to get the desired result?

Great thanks to those who answer.

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 Post subject: Re: On general approach to solvingPosted: Thu Sep 20, 2012 12:34 pm

Joined: Sun Aug 26, 2012 10:01 am
I'm going to be doing this when I buy David Pitcher's Pentamid Sorry if you were hoping this reply was from an experienced solver

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 Post subject: Re: On general approach to solvingPosted: Thu Sep 20, 2012 1:35 pm

Joined: Thu Dec 15, 2011 10:04 pm
1. When you get the new puzzle do you twist it from solved state and back in order to understand how pieces move and find proper algorithms and then scramble and solve or you scramble it immediately?
Yes, I do as you describe. I look at the puzzle and determine what algorithms might be useful. Then I try the algorithms and record the results. I often take photos. I don't deliberately scramble a puzzle until I have some idea of how I will solve it.

2. When exploring how pieces move from scrambled state do you need to make records in order to understand which pieces moved and which did not or you can keep all the state in memory?
On new, difficult puzzles I take photographs, make diagrams and write notes during the initial solve. A few puzzles require complex setup moves that I write down (e.g. Face Turning Starminx and some Crazy 3x3s).

3. When puzzle contains many identical pieces do you use something to differentiate one from another and understand which of them exactly are moving (like pieces of plaster)?
I use coloured dots and bits of painter's tape. It is very important to understand what an algorithm does, but applying algorithms in the solved state sometimes doesn't show everything.

4. How you find algorithms? Just trying several commutators learning what they do and then trying to combine with setup moves and each other in order to get the desired result?
Exactly as you described. I try things I already know and adjust. I developed a corner 3-cycle for the Pentahedron series by starting with a cuboid corner swap and I came up with several algorithms for the Tuttminx based on Megaminx algorithms. It's not easy and after some reasonable effort on my own, I will watch YouTube videos or read TP forum to get more ideas. I still like watching tutorials, but I try to wait until after I know how to solve a puzzle.

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 Post subject: Re: On general approach to solvingPosted: Thu Sep 20, 2012 4:52 pm

Joined: Mon Feb 28, 2011 4:54 am
Quote:
1. When you get the new puzzle do you twist it from solved state and back in order to understand how pieces move and find proper algorithms and then scramble and solve or you scramble it immediately?

Almost never scramble immediately. I'm far too scared I'll never get it back. Sometimes when I'm fairly confident I'll be able to solve it, I'll scramble it.

Quote:
2. When exploring how pieces move from scrambled state do you need to make records in order to understand which pieces moved and which did not or you can keep all the state in memory?

From scrambled state, there's no way I can keep things in memory.

Quote:
3. When puzzle contains many identical pieces do you use something to differentiate one from another and understand which of them exactly are moving (like pieces of plaster)?

Often I'll carry out an algorithm and keep my eye on one particular piece to follow where it ends up, and then write that down (eg. UFL). Then do the same alg again and write its new location down. Until it arrives back where it started. Occasionally I've bluetacked tiny bits of paper with numbers onto pieces.

Quote:
4. How you find algorithms? Just trying several commutators learning what they do and then trying to combine with setup moves and each other in order to get the desired result?

By firstly trying familiar algorithms. and then trying variations on them. One of my most cherished memories of doing this is coming up with a 3-cycle on the crazy saturn 3x3x3 cube (seems like a long time ago!). But if this doesn't work, the other way to find algorithms is by looking on relevant TP threads.

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 Post subject: Re: On general approach to solvingPosted: Tue Oct 23, 2012 12:36 am

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
Shrike wrote:
Several questions for experienced solvers, if possible:

1. When you get the new puzzle do you twist it from solved state and back in order to understand how pieces move and find proper algorithms and then scramble and solve or you scramble it immediately?

I always can't resist scrambling a new puzzle immediately, and then try to solve it without knowing how beforehand. I have been known to get stuck for a while because I never figured out any algorithms for the new puzzle yet. But that's part of the fun of discovery -- I feel like I'm actually discovering how to solve it rather than already knowing everything beforehand.

Quote:
2. When exploring how pieces move from scrambled state do you need to make records in order to understand which pieces moved and which did not or you can keep all the state in memory?

When starting on an unknown puzzle, I always use commutators, which only affects a minimal number of pieces at a time. The way they move the pieces is usually quite predictable.

Quote:
3. When puzzle contains many identical pieces do you use something to differentiate one from another and understand which of them exactly are moving (like pieces of plaster)?

No, I consider that cheating. I do keep in mind, though, that identical pieces mean that you may run into parity problems later on, so when I get into a situation that looks like it's a parity problem, then I know to try to swap two of the identical pieces in order to "fix" the parity.

Quote:
4. How you find algorithms? Just trying several commutators learning what they do and then trying to combine with setup moves and each other in order to get the desired result?

I solved every puzzle I have using commutators only. Well, except for the big even cubes, which require one a special edge-flip algo (that I discovered on my own). Commutators are amazing... you can literally solve almost any puzzle with them, and the way they move pieces around usually follows a predictable pattern. Sometimes you can even successfully solve a particular situation just by guessing what the commutator might be.

Quote:
Great thanks to those who answer.

Sorry for the late reply, I haven't been on the forum for a while.

I just like to add another note: although commutators can work for just about anything, there is another level of consideration that needs to be taken into account if you're going to solve the entire puzzle. Commutators pretty much almost guarantee that a particular subset of the puzzle (say all edges, or all corners) are solvable. But it may not be very obvious how to solve the rest of the puzzle without touching what you just did. For example, for the FTO (face-turning octahedron), the corners can be easily solved using commutators, but the commutators also permute the face centers in a non-trivial way. When a situation like that arises, usually the solution is to change the order you do things (e.g., don't do face centers first, since they will get messed up when you do corners; do corners first then face centers, and you avoid the problem).

So on one level, it's all just commutators; but on another level, there is also the question of what to solve first, because sometimes it matters.

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 Post subject: Re: On general approach to solvingPosted: Tue Oct 23, 2012 5:53 am

Joined: Sun Mar 27, 2005 7:37 pm
I can only really go back to the first ever Rubik's Cube I owned.
The idea of not scrambling a puzzle in order to find a solution seems so incredibly wrong to me and would be like cheating since the idea is to solve it, not start with it solved, but each to their own. So yes of course I scrambled as fast as I could and then started solving. I guess the first road block was how to deal with bottom corners after you have a top side completed. The only way I could figure it out was to break up the side in as simple way as possible and then remake it in a slightly different way while recording the moves on paper. I could then see what effects the whole sequence of moves had.
The other breakthrough idea I had was if I take an edge for example out of the top side and then put it back flipped, I could then turn the top side, repeat the move in reverse and in theory everything else should go back to the way it was leaving my two edges flipped. Amazingly it worked.
So my two logical approaches above combined with some intuitive stuff is my basis for solving puzzles when I can be bothered these days.

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 Post subject: Re: On general approach to solvingPosted: Tue Oct 23, 2012 12:24 pm

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
Tony Fisher wrote:
[...]
The other breakthrough idea I had was if I take an edge for example out of the top side and then put it back flipped, I could then turn the top side, repeat the move in reverse and in theory everything else should go back to the way it was leaving my two edges flipped. Amazingly it worked.
[...]

Actually, this is known as conjugation, and in principle always works. I forgot to mention this in my post... commutators are great, but sometimes tedious if the pieces just aren't in the right places/orientation. So you move that one piece which is in the wrong orientation around the puzzle a bit, while keeping the other pieces fixed, until it comes back in the right orientation, then do the commutator, then reverse what you did to that piece.

Side story. Some years ago I was teaching my roommate how to solve the 3x3x3, and the last step in my method was to position and orient the last 3 corners simultaneously with a single commutator. This required that all the corners be in exactly the right orientations, but they often aren't. So I told him, you just move that third corner down to the bottom layer, twist it into another orientation, and bring it up again, then do the commutator -- and the cube looks completely messed up again at this point -- but then you just reverse what you did to that third corner, and suddenly everything just comes together and the cube seemingly magically pops out solved. He was suitably impressed.

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 Post subject: Re: On general approach to solvingPosted: Wed Oct 24, 2012 8:10 am

Joined: Sun Mar 27, 2005 7:37 pm
quickfur wrote:

Side story. Some years ago I was teaching my roommate how to solve the 3x3x3, and the last step in my method was to position and orient the last 3 corners simultaneously with a single commutator. This required that all the corners be in exactly the right orientations, but they often aren't. So I told him, you just move that third corner down to the bottom layer, twist it into another orientation, and bring it up again, then do the commutator -- and the cube looks completely messed up again at this point -- but then you just reverse what you did to that third corner, and suddenly everything just comes together and the cube seemingly magically pops out solved. He was suitably impressed. :)

I often get non puzzling friends asking me how I solved the cube. I try to explain in similar ways to what you wrote but they can never understand the logic which seems so obvious to me. I can see that I've lost them after a few seconds and I'm thinking, "well don't ask then"! It might be an age thing I guess because none are very young.

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 Post subject: Re: On general approach to solvingPosted: Wed Oct 24, 2012 9:51 am

Joined: Wed Jan 14, 2009 6:37 pm
Location: The Great White North
Tony Fisher wrote:
quickfur wrote:

Side story. Some years ago I was teaching my roommate how to solve the 3x3x3, and the last step in my method was to position and orient the last 3 corners simultaneously with a single commutator. This required that all the corners be in exactly the right orientations, but they often aren't. So I told him, you just move that third corner down to the bottom layer, twist it into another orientation, and bring it up again, then do the commutator -- and the cube looks completely messed up again at this point -- but then you just reverse what you did to that third corner, and suddenly everything just comes together and the cube seemingly magically pops out solved. He was suitably impressed.

I often get non puzzling friends asking me how I solved the cube. I try to explain in similar ways to what you wrote but they can never understand the logic which seems so obvious to me. I can see that I've lost them after a few seconds and I'm thinking, "well don't ask then"! It might be an age thing I guess because none are very young.

I was lucky. My roommate was the first person I tried to teach, and he actually understood what I was saying and did manage to learn how to solve the 3x3x3. He tried doing the 4x4x4 but got hung up on the parity issues and gave up shortly after. After that, though, others that I tried to teach got lost halfway through (or before). It's only recently that I managed to get a second "student" to successfully learn how to solve the cube -- though in this latter case he already learned a bunch of stuff from youtube, so I guess it doesn't really count.

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