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Calculating "The Devil's Algorithm"

shadowslice e

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You do realize that RU and UR are in fact the same. If "U" were 3, and "R" were 2, then UR (3*2) would equal 6. Similarly, RU (2*3) would equal 6.
Also, g*b+g*a is the same as g*a+g*b as bedmas states to do multiplication first.

Not with matrix multiplication. With that you must have a specific order as AB does not equal BA unless B is the inverse of A or the identity matrix. And we have to use matricies to describe the transformations.

Thus, the cycle length may be the same for the example you provided because they are only length 2. If you try a longer one, you will find that something like R U R' U' does not have the same cycle length as R R' U U' despite bidmas/bodmas/bedmas saying that they would be the same as those acronyms only work for pure algebra with no matricies.

In fact, the only reason U R and R U have the same number is due to the symmetries that the two generators have (ie. Rotated 90 then reflected.)
 
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guysensei1

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You do realize that RU and UR are in fact the same. If "U" were 3, and "R" were 2, then UR (3*2) would equal 6. Similarly, RU (2*3) would equal 6.
Also, g*b+g*a is the same as g*a+g*b as bedmas states to do multiplication first.

Pick up 2 cubes, do UR on one and RU on another and convince yourself that you're wrong :)
 

DELToS

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Well, I did find an alg for 5x5 that you would have to repeat 556,920 times to get it back to the solved state:
R2 B' D' U Bw2 L Rw2 U' Dw2 Fw2 R2 Lw2 B R L2 Lw L2 R2 F' Fw2 R' Rw Lw D' F2 Dw2 L' D2 Bw' Rw' D2 B Fw2 Rw R' Uw L2 Rw2 Lw F' Fw U Fw2 L' Rw' Uw' U' F2 Dw' Fw' L' U2 Dw' D2 B2 R Uw' Lw2 U' Rw' L2 Dw2 U2
 

qqwref

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Just for anyone who's curious, the highest possible order (number of times to repeat a sequence) on the 5x5x5 is 281,801,520, and one such sequence is B' Dw D2 R' Dw Uw' B Dw' D B' Dw' Uw R B R2 Rw Dw2 Uw2 Fw' Lw' Fw2 Lw Fw Lw Uw' Fw' Lw' Fw2 Lw (source)

Or, Fw F' Rw' R L2 F2 B U2 Dw D' Lw L' R F U (source)
 

guysensei1

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Just for anyone who's curious, the highest possible order (number of times to repeat a sequence) on the 5x5x5 is 281,801,520, and one such sequence is B' Dw D2 R' Dw Uw' B Dw' D B' Dw' Uw R B R2 Rw Dw2 Uw2 Fw' Lw' Fw2 Lw Fw Lw Uw' Fw' Lw' Fw2 Lw (source)

Or, Fw F' Rw' R L2 F2 B U2 Dw D' Lw L' R F U (source)

What about 3x3 or 4x4?
 

Sajwo

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For 4x4 it's 765 765 and for 5x5 281 801 520. Don't know how accurate these numbers are since I didn't calculated that. Found it on Polish forum. If you add rotations, it will be probably twice as that.
 

AlexanderGZH

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assuming your "god's algorithm" g exists:
then R=g*a (repeating gods alg a times, for a certain a) and U=g*b (similar)
so RU=(g*a)+(g*b)=g*(a+b)=g*(b+a)=g*b+g*a=UR
as RU is not the same as UR i prooved that your "gods algorithm" cannot exist.
Should R or U be the superflip position, it can exist. Superflip is the only position(other than solve which is equivalent to doing nothing) in 333 with this commutative property. It's like(for matrices) IX=XI where I is the identity matrix and can only be the identity matrix
 

EminentCuber

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This is a very interesting theory, but I would start trying this with a 2x2.

Secondly, god's algorithm refers to if you solved it like a god, how many moves you would do (the most optimal case.) What you're talking about is actually devil's algorithm, which refers how a devil would solve it (really poorly and lazily.)

If I can show some light, whatever light it is, I would think that devil's algorithm has to be super long (and I mean like, 1 trillion turns) and will most likely appear very random to a normal human and express no pattern at all.

It's going to take a lot of math, headaches and lines of code to figure this one out.

And if you have a 2x2x1 or a floppy cube, something with very few (probably around <20) you could test this theory out on and probably do it manually, without the assistance of a computer.

Devil's algorithm will most-likely have no or, at the very least, very little applications. It will be absolutely pointless to use this to solve a Rubik's cube, you're better off just using Ruwix.com.

anyway, good luck with this.
~EminentCuber
 
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@EminentCuber: Try reading the thread. It's already been done for 2x2 and 3x3 (as well as some other simple puzzles) and linked to here. Also, judging by your post, you might want to have a look around and read up on some cube theory. The Devil's algorithm isn't supposed to be useful for solving, it's just interesting.
 

00

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This is a very interesting theory, but I would start trying this with a 2x2.

Secondly, god's algorithm refers to if you solved it like a god, how many moves you would do (the most optimal case.) What you're talking about is actually devil's algorithm, which refers how a devil would solve it (really poorly and lazily.)

If I can show some light, whatever light it is, I would think that devil's algorithm has to be super long (and I mean like, 1 trillion turns) and will most likely appear very random to a normal human and express no pattern at all.

It's going to take a lot of math, headaches and lines of code to figure this one out.

And if you have a 2x2x1 or a floppy cube, something with very few (probably around <20) you could test this theory out on and probably do it manually, without the assistance of a computer.

Devil's algorithm will most-likely have no or, at the very least, very little applications. It will be absolutely pointless to use this to solve a Rubik's cube, you're better off just using Ruwix.com.

anyway, good luck with this.
~EminentCuber

please stop bumping old threads without contributing anything
 
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