God's Number in QTM is 26

Herbert Kociemba

Member
I just had the idea: I wonder what God's number is if we exclude all primes? So just R and R2 are allowed, not R'. Of course, we could require R2 and R' because of symmetry, but that is indifferent.
If R and R2 count as 1 move, then R' counts as 2 moves in the metric you suggest. In QTM R and R' count as one move and R^2 counts as 2 moves. If you count the number of canonical maneuvers for each length you get the same distribution as in QTM and hence the same lower bound which is 21 (see http://cubezzz.duckdns.org/drupal/?q=node/view/236). I suspect Gods number in the neighborhood of Gods number for QTM.

Robert-Y

Member
Hm, an update to CubeExplorer for finding sub-optimal and optimal solutions in QTM might be a good idea!
But on the other side... How many actually would use it?
You have no idea how much I would use this. Also if it had the option to ignore all post U moves, then we basically have the perfect program for finding speed optimised algorithms.

Herbert Kociemba

Member
You have no idea how much I would use this. Also if it had the option to ignore all post U moves, then we basically have the perfect program for finding speed optimised algorithms.
What do you mean with "ignore post U moves" ?

Musicalboy2

Member
What do you mean with "ignore post U moves" ?
I think he means U moves after an alg, like that which would usually be called AUF rather than part of the alg itself.

Robert-Y

Member
^Yes, most of the time we don't care about any U turns at the end of an algorithm. For example, every LL algorithm that we all learn does not include a U/U'/U2 at the end of the algorithm. Most of the time, I do not want any U turn at the end of an algorithm to contribute to its move length.

Herbert Kociemba

Member
Most of the time, I do not want any U turn at the end of an algorithm to contribute to its move length.
Ok, I understand. I suppose you work with the module for incomplete cubes to generate the algorithms. If you search for example for an algorithm of length 12, in the current version you also have to look at the maneuvers of length 13 which end in an U, U2 or U' move. But is that really so uncomfortable?

Musicalboy2

Member
Ok, I understand. I suppose you work with the module for incomplete cubes to generate the algorithms. If you search for example for an algorithm of length 12, in the current version you also have to look at the maneuvers of length 13 which end in an U, U2 or U' move. But is that really so uncomfortable?
I haven't done nearly as much work on algs as Robert Yau has, but from my very limited experience, the longer the algs get, the more time the program takes. So I'm thinking that while it might not seem at all significant for searching length 12/13, perhaps, say, length 17/18 there is a significant difference, and you really just end up sifting through more algs... He also did use the word "perfect", so perhaps there's little difference, but would be a nice feature to have anyway.

While we're on the topic of cubeexplorer, I'd actually really love a feature where the program can deduce and fill in the missing stickers - it doesn't seem like it should be hard to automate, and it'd make reconstructions (without scrambles) easier.

Christopher Mowla

While we're on the topic of cubeexplorer, I'd actually really love a feature where the program can deduce and fill in the missing stickers - it doesn't seem like it should be hard to automate, and it'd make reconstructions (without scrambles) easier.
Your request is equivalent to saying there is only one solution to the equation x + y= 100. You have to assume a value for either x or y in order to solve this equation.

Similarly, Cube Explorer would have to assume the position meant by a user, but it isn't always straightforward which position should be assumed, as there is more than one possibility in many cases.

If Cube Explorer assumes the wrong position (which is more than likely), what good is the reconstruction? If it gives you all possible positions, are you willing to search through all of them to find the correct one?

Musicalboy2

Member
Your request is equivalent to saying there is only one solution to the equation x + y= 100. You have to assume a value for either x or y in order to solve this equation.

Similarly, Cube Explorer would have to assume the position meant by a user, but it isn't always straightforward which position should be assumed, as there is more than one possibility in many cases.

If Cube Explorer assumes the wrong position (which is more than likely), what good is the reconstruction? If it gives you all possible positions, are you willing to search through all of them to find the correct one?
I mean those colours which it can deduce, of course. Say you have two known stickers on a corner, and a colour scheme. Only one possible sticker can go in the remaining spot. Or say you have 3 known white-(colour) edges and one white-blank edge. Obviously there's only one colour left. This isn't hard for a human to figure out, but still somewhat time consuming. Or I'm slow. but either way...

Edit: Or the worst, I think, is if you had just one piece left, completely blank. There's only one way this piece can be placed to make the cube solvable, but yet unless I fill in the piece, cubeexplorer will try to find an optimal solution, which is often really slow.

Last edited:

Herbert Kociemba

Member
I mean those colours which it can deduce, of course. Say you have two known stickers on a corner, and a colour scheme. Only one possible sticker can go in the remaining spot. Or say you have 3 known white-(colour) edges and one white-blank edge. Obviously there's only one colour left. This isn't hard for a human to figure out, but still somewhat time consuming. Or I'm slow. but either way...

Edit: Or the worst, I think, is if you had just one piece left, completely blank. There's only one way this piece can be placed to make the cube solvable, but yet unless I fill in the piece, cubeexplorer will try to find an optimal solution, which is often really slow.
There is the "autofix colors" options, I just tried it and it seems indeed to be broken or does not work correctly. I will put this onto the todo list. Pieces which can be uniquely be identified though some stickers are missing should indeed be completed with this option selected.

Swordsman Kirby

Member
Heh, I saw Morley Davidson get called up to the staff area before the announcement, and I asked him "God's number for QTM?" and he responded with something like "did I give it away already?"