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EdCollins
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May 31st, 2018 at 5:08:55 AM permalink
Quote: GWAE

Ed, have you timed yourself on the old vs new? Curious how it changed your speed, if any.

Nope, I haven't timed myself yet and my other speedcubing cubes are such good fast, smooth cubes that these new magnetic times won't shave off anything measurable. For me, the only way to drastically reduce my time is to learn a faster method entirely. I'm STILL solving cubes with the darn Beginner's Method. CFOP (Fridrich) and Petrus an ZZ, and even Corners First, from what I've read, all require less moves, and once I learn the method, will be ultimately faster.
EdCollins
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June 2nd, 2018 at 1:58:00 AM permalink
Hi Mike,

I contest your "If a monkey was playing with a Rubik's Cube" answer, in your wonderful "Ask the Wizard" column, located on this page: https://wizardofodds.com/ask-the-wizard/268/

1) First, the equation (8! × 12! × 38 × 212) does not equal 519,024,039,293,878,000,000.

2) Second, the equation (8! × 12! × 38 × 212 / 12) does not equal 43,252,003,274,489,900,000.

The answer that you arrived at is the desired answer for the column, for the point you are making, but as written, the equations are wrong. However, it's just a formatting problem. What's going on the formatting for both of these equations was probably lost/changed. The equations should be 8! × 12! × 3^8 × 2^12.

(I thought I'd point that out, but that is not what I'm contesting.)

Based upon the method of determining the number of different permutations of a Rubik's Cube, if I pick up a scrambled cube from the table, and then immediately place it back down again, without turning any of the faces before putting it down, but I put it down with a different side face up than the side that was face up when I first picked it up, that's considered a different permutation.

And that's fine. I'm okay with calling that a different permutation. Yes, the cube is in the same state, i.e. it's considered the same scramble, but if we want to call that a different permutation, I won't argue.

However, if we do call that a different permutation, then we "can't have our cake and eat it too."

To illustrate, assume we now pick up a completely solved cube from the table, and immediately put it back down, again, without turning any of the faces, and we also put this cube down with a different side face up than it was when we picked it up. This must also be considered a different permutation.

This means that of the 43 quintillion plus possible permutations, we must consider 24 of these to be in the "solved state!"

I say 24, because 6x4 = 24. There are six sides to each cube. We can put it down with a total of six different sides face up. And I can also pick up a scrambled cube from the table and place it down with the same side face up, but this time I place it back down with one of the faces in a different direction. (For example, if I place the side that was pointing east now to the south.) There are four different "directions" to place it back down. That would also be considered a different permutation. (It doesn't appear as if it is a different permutation with a solved cube, of course, but it's apparent with a scrambled cube.)

Thus, when you state that "seven billion monkeys randomly playing with the cube at a rate of one rotation per second, will pass through the SOLVED POSITION once on average every 196 years" I contest that answer. I submit that you are overstating the frequency by a factor of 24. There are actually 24 solved states if there are 43,252,003,274,489,856,000 permutations.

So either the number of monkeys (7 billion) are overstated by 24 or the time period (196 years) is overstated by 24.

(The number of seconds in 196 years x 7 billion monkeys does equal 43 quintillion (roughly), so the answer was correct otherwise.)

What do you think?
Wizard
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June 2nd, 2018 at 4:16:30 AM permalink
As to your first point, thank you. Somehow the superscripts got lost so 38 came out looking like 38, for example. That problem has happened many times before.

However, I maintain the intended answer is right. The centers are always fixed on the cube. There is only one way to arrange all the other pieces given the locations of the corners. You'll notice I don't multiply by 24 for the 24 ways the corners could be facing in each direction. Thus I don't need to divide by it.

Furthermore, my figure matches other sources on the topic and I don't think I would we would all be making this error.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
EdCollins
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June 2nd, 2018 at 8:59:01 AM permalink
I'm not at all disputing the 43 quintillion number. It's correct. And I know the centers are always fixed. In fact, what is interesting is that of ALL the scrambled states, the red center face is ALWAYS opposite the orange center face AND the blue center face is ALWAYS opposite the green center face AND the yellow center face is ALWAYS opposite the white center face!

Knowing that, you could perform a simple "magic trick" on a very young child or someone who is unfamiliar with the cube, who doesn't understand this. You could turn your back on them and ask them to scramble the cube and without looking at it, with some clever banter and some fake "hocus pocus," you could then "predict" for them that with their scrambled cube, the red center face is opposite of orange, blue is opposite of green, etc.

This would only "baffle" them for just a moment of course... since they would quickly realize that any and all scrambles have this property!


Anyway, so picking up a cube and simply rotating it 90 degrees and putting it back down without turning any of the sides does NOT count as a different permutation, then, correct?
EdCollins
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June 2nd, 2018 at 9:05:46 AM permalink
How may different permutations are possible given the numbers 1-2-3 ?

The answer is easy. Three factorial, or six. We all know this. The number is small enough we can quickly list them: 1-2-3, 1-3-2, 2-1-3, 2-3-1, 3-1-2, and 3-2-1.

So, consider this as an actual two-dimensional puzzle. Write down a 1 on a tiny piece of paper and a 2 on another tiny piece of paper, and a 3 on another piece of paper. There are still six different ways to arrange the numbers, yes? Six permutations.

Now, given the criteria that a solved state of this puzzle "consists of the numbers in numerical order, from smallest to largest," how many solved states are there?

The answer, which will be apparent in a moment, is two, not one!

It cannot be over-emphasized that we are dealing with a physical two-dimensional puzzle here. (Two dimensions, of course, for this example, since our tiny pieces of paper have length and width but no depth.)

These two permutations:

1-3-2 and 2-3-1

no matter how I look at it or view it doesn't meet the solved state criteria.

Likewise with these two permutations:

2-1-3 or 3-1-2

Ah, but if I arrange my tiny pieces of paper this way:

1-2-3 or 3-2-1

both of these perms are solved states!

Wait! Why? Why is 3-2-1 a solved state? The numbers aren't in order from smallest to largest?

Although it doesn't look like a solved state from my point of view, to a person standing directly across from me, looking at me, they DO see the puzzle in a solved state! Whereas I see a 3 on the left, they see a 1 on the left.

To clarify, again recall we are talking about a physical puzzle. In fact, if this tiny puzzle were thin magnet pieces (for example) that could actually touch and connect to each other, and if this device/puzzle were designed to "light up" or "make a sound" when a solved state was reached, it would light up/make a sound when a 1-2-3 arrangement was reached and when a 3-2-1 arrangement was reached. (It must, of course. The puzzle wouldn't know how you are viewing it!)

So any description with THIS little puzzle that mentions monkeys moving these little pieces around randomly, would have to state that they would find a solved state 2/6 of the time, not 1/6.



However, it sounds as if all of this was taken into account when determining the cube's 43 quintillion plus permutations, yes??? It sounds as if mirror arrangements and simple puzzle rotations are NOT considered an entirely different permutation. (Because if they were you would have to consider the solved state permutations too.)
Wizard
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June 2nd, 2018 at 9:24:31 AM permalink
Quote: EdCollins

Knowing that, you could perform a simple "magic trick" on a very young child or someone who is unfamiliar with the cube, who doesn't understand this. You could turn your back on them and ask them to scramble the cube and without looking at it, with some clever banter and some fake "hocus pocus," you could then "predict" for them that with their scrambled cube, the red center face is opposite of orange, blue is opposite of green, etc.



That would be too intellectually lazy for a magic trick, at least for me. My favorite easy magic trick on young kids is the "coin in your ear" one. Works every time. Reminds of this Calvin and Hobbes comic strip.

Quote:

Anyway, so picking up a cube and simply rotating it 90 degrees and putting it back down without turning any of the sides does NOT count as a different permutation, then, correct?



That is correct.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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June 4th, 2018 at 6:37:29 PM permalink
Time to move onto the tetrahedron puzzles. The first is the 2x2 Pyraminx. This is a hard one to explain how to solve so go easy with your comments, please.


Direct: https://youtu.be/JhEw_G7EZx0
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
billryan
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June 4th, 2018 at 6:44:27 PM permalink
Have you seen the video of the young guy solving cubes while juggling?
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EdCollins
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June 4th, 2018 at 6:55:36 PM permalink
Quote: billryan

Have you seen the video of the young guy solving cubes while juggling?

Yes, I did. That video seemed to hit all of the major news sites.

Over the past few weeks, I've probably watched more 50-75 YouTube videos related to the Cube. I'm not kidding.

I've watched tutorials on how to solve it, via various methods. (CFOP, Roux, ZZ, Corners First, etc.)
I've watched videos of three-year-olds solving it.
I've watched it being solved blindfolded or with one hand or underwater.
I've watched videos taken at various competitions.
I've watched it being solved in less than ten seconds by dozens of different individuals.
I've watched reviews of all of the different brands of cubes you can purchase.

For whatever reason, each night for the past couple of weeks, when I had a free moment or two, I would find myself searching out new Cube videos! This thread is invariably the cause of that. It reignited my long-time interest in Rubik and his cube.

Fortunately, I think I'm done watching videos!
beachbumbabs
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June 4th, 2018 at 7:39:20 PM permalink
Quote: billryan

Have you seen the video of the young guy solving cubes while juggling?



How odd you mention that. I just sent it to Mike this morning.
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Wizard
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June 4th, 2018 at 8:02:04 PM permalink
Quote: beachbumbabs

How odd you mention that. I just sent it to Mike this morning.



Barb sent me one of an Asian boy doing it. I've seen another video of someone else doing it. Sure puts me to shame.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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June 7th, 2018 at 10:10:52 AM permalink
Quote: beachbumbabs

How odd you mention that. I just sent it to Mike this morning.



Three people have so far.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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June 7th, 2018 at 10:12:01 AM permalink
Here is my latest video on the Pyraminx (not to be confused with the smaller 2x2 Pyraminx I did in my previous video). This one is actually easier.


Direct: https://youtu.be/ZITQoMk0QZo
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Rigondeaux
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June 7th, 2018 at 5:28:27 PM permalink
I had no idea what cubing is so i looked it up.

Wizard
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June 30th, 2018 at 3:45:12 PM permalink
Here is my solve of the 4x4 Pyraminx. This video was one of the tougher ones to make.


Direct: https://youtu.be/J27y5rvd3rw
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
gordonm888
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June 30th, 2018 at 4:22:28 PM permalink
Quote: Rigondeaux

I had no idea what cubing is so i looked it up.



LOL, rigondeaux, do not get on google videos and search on that - because the video you get will be unspeakable.

By the way, without watching these videos all the way through I have to praise how far these videos have come. They are much more polished in almost every way and are looking quite good (given the subject matter.) So, as a former nitpicker critic I now say "Looking good!"
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
Wizard
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June 30th, 2018 at 5:31:45 PM permalink
Quote: gordonm888

By the way, without watching these videos all the way through I have to praise how far these videos have come. They are much more polished in almost every way and are looking quite good (given the subject matter.) So, as a former nitpicker critic I now say "Looking good!"



Thank you Gordon. Once I get through all my puzzles, I plan to start redoing these videos one at a time.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
Wizard
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July 1st, 2018 at 9:41:23 PM permalink
I couldn't sleep well at night with that 4x4 Pyraminx video. It was simply not up to my usual low standards. So, I redid it. Here is the new and improved version.


Direct: https://youtu.be/8bQmGJjYvME

If you're asking, "How could this possible be better than anything?," then the answer is it has fewer verbal mistakes, is shorter, and the previous one forgot to mention an important algorithm.
Last edited by: Wizard on Jul 2, 2018
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
AxelWolf
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July 2nd, 2018 at 3:18:15 AM permalink
Quote: Rigondeaux

I had no idea what cubing is so i looked it up.

I skipped to the last page and the first post was:

Quote: Wizard

Barb sent me one of an Asian boy doing it. I've seen another video of someone else doing it. Sure puts me to shame.



Anyways, in the poll I voted, I feel pretty

Enjoy.

♪♪Now you swear and kick and beg us That you're not a gamblin' man Then you find you're back in Vegas With a handle in your hand♪♪ Your black cards can make you money So you hide them when you're able In the land of casinos and money You must put them on the table♪♪ You go back Jack do it again roulette wheels turinin' 'round and 'round♪♪ You go back Jack do it again♪♪
Wizard
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July 2nd, 2018 at 7:49:33 AM permalink
If "cubing" meant the pursuit of "cubs," then shouldn't it have been spelled cubbing? As in "You're rubbing me the wrong way."

I probably didn't help things with the "I feel pretty" choice, but it was supposed to be a reference to the movie.

"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
EdCollins
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July 6th, 2018 at 8:17:35 PM permalink
Wiz, I'm curious... did you ever splurge and get yourself an expensive 3x3x3 cube, possibly one with those tiny magnets inside?

To refresh your memory, back in May I purchased a cube with magnets (a Valk 3 Power M, stickerless), from thecubible.us, and I really, really like it a lot. It's a joy to play with. It's well worth the $38.99 I spent on it.
Wizard
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August 9th, 2018 at 7:49:19 AM permalink
Quote: EdCollins

Wiz, I'm curious... did you ever splurge and get yourself an expensive 3x3x3 cube, possibly one with those tiny magnets inside?



No, I still haven't. I guess I wasn't sure which one to get, so thank you for the recommendation.

In new news, I just posted a video on how to solve the 4x4x4 up to the last layer. Enjoy!


Direct: https://youtu.be/QkDroVSaxmU
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
GWAE
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February 21st, 2019 at 9:24:52 AM permalink
https://www.facebook.com/106917292698829/posts/2427968707260331/
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gamerfreak
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February 21st, 2019 at 9:49:02 AM permalink
Since posting in this thread last I have solved my cube a number of times. Itís really pretty easy to repeat after youíve done it once.

I donít have the fortitude to learn to do it by memory, but this at least checks a small item off my bucket list.
Wizard
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February 21st, 2019 at 1:34:01 PM permalink
Quote: gamerfreak

Since posting in this thread last I have solved my cube a number of times. Itís really pretty easy to repeat after youíve done it once.

I donít have the fortitude to learn to do it by memory, but this at least checks a small item off my bucket list.



Congratulations! Not to diminish your accomplishment, but to get full credit, you have to do it from memory.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
heatmap
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April 13th, 2019 at 7:18:58 AM permalink
A RUBIKS CUBE THAT IS ALSO ROULETTE!!!!

http://www.dudeiwantthat.com/entertainment/games/roulette-wheel-iq-cube.asp
onenickelmiracle
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September 21st, 2019 at 10:02:51 AM permalink
I don't know how to solve a rubik's cube. I don't think I'm any better at them now than when I was 8 years old, and might even be worse.
I am a robot.
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