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is it possible those difficult positions are solvable in less moves if you tried to do them in another orientation, since an FTO doesn't have a fixed centers if you do outer layer moves? or did you already take that into account

let me phrase this like this, imagine there is a case generated by R U that can’t be done in 24 moves in F R U, but can be in BR R U, let’s call it the annoying case now when we solve Megaminx Gen <F, R, U>, we first solve block+EO and then that fake Gen <R, U>, that’s the best we can do on a...

to verify the bound of 24 for the purposes of the Gen <F, R,U> God's number, we need to solve all those 25-move <R,U> cases in <F,R,U> in 24 moves or less what Rokicki did, essentially, is to do them in <F,R,U>, we try to get them down to 24 moves, and if that didn't work, do them in <BR,R,U>...

yes but in improving the bound of the last stage to 24, you'd need to confirm that all the 25-movers in Gen <R, U> can be done in less moves in Gen <F, R, U>, but Rokicki used <F, R, U> and <BR, R, U> intermittently as far as I'm aware, if a particular case couldn't be handled in sufficient...

Ok then so a bound of 42 for <F, R, U> is confirmed then, with your block+EO and then Ben's <R, U> 26 confirmation followed by Rokicki's improvement down to 25, so 17 + 25 = 42.

By restriction I mean literally a restriction of the kinds of moves you are allowed to do, like this <F, R, U> where you can only do turns on the front, right, and upper faces. I assumed that during that stage you were limited to those 3 faces, but I realized that I didn't actually know that...

I just wanted to point out that the work done here also shows an upper bound for Gen <U, F, R> on Megaminx of 41 moves. That's 17 moves from Alexander Botz's analysis of the stage of 2nd last S2L face + EO, and Ben's Gen <U, R> God's number of 26, pushed to 24 by Rokicki's exclusion of the...

For the record, I'm using the number of positions as calculated by Christopher Mowla in 2014. Here in 2021 he shared a concise WolframAlpha equation for it for any big minx.

My program creates a list of all the categories. For big minxes it’s not so bad. There’s still four categories from Megaminx, of 1, 2a, 2o, and 3, it’s just that now you also have to take how many layers were turned. So say for teraminx, category 3 where one face had 1 layer turned, second had...

So another insight. I decided to stop using Google Sheets spreadsheets for doing these tables, all of only have precision up to 15 digits and I wanted to be sure my numbers were actually correct, I don't think I had much to worry about, I would later compare the results for Megaminx and they...

How do you calculate the recurrence relation? that result for the Megaminx seemed like magic, I get the result for 3x3 (f(n)=12*f(n-1)+18*f(n-2) for n>=3)and the big cubes (f_m(n) = sigma m-1 p=1 (m-1)!/(p!(m-1-p)!)*2*3^p*f(n-p) for mxmxm and n<=m), it makes logical sense, but it was a little...

Anyway, I just calculated the lower bound for God's number for the Tuttminx. For those unfamiliar Tuttminx is a puzzle similar in spirit to the Megaminx but which has 32 faces, 12 pentagonal and 20 hexagonal, its shape is called in math the truncated icosahedron and is the pattern visible on...

if I understand this correctly... you have the tool to compute, say, tuttminx's and futtminx's lower bound easier? it's notoriously hard to do using this method, I counted 104 different categories before I gave up cataloguing them by hand, which would've later involved checking through how they...

Funnily enough, neither the metric used by masonjones nor by you is the one actually used to count moves on the Square-1 by the WCA as defined in 12c4* for the purposes of rule 4b3d**. Would it be possible to say what the God's number is using WCA's knock-off Axis Turn Metric? Using the result...

no shot, so the known upper bound really is 116 then?

I'm getting 8 stages, 3 for F2L, 4 for almost S2L plus EO, and final 2 Gen <R,U> stage, i.e. the ones I listed above and which give the upper bound which give 117 as the upper bound, that's the "method" I am referring to and the one I frankly was the most curious about. You say your method now...

for your project, I imagine it's done in less stages, I meant for the theoretical best known solving method defined by the lowest upper bound

the way I understood it, the solving is done in 8 stages, firstly of category Phase1 which is F2L, so "Phase1Block1" is a 2x2x2, "Phase1Block2" is F2L minus a 3x2x1, "Phase1Block3" is full F2L, then Phase2 is almost full S2L save for last face (plus the top face of course), so "Phase1Block1" is...

have you considered trying to calculate the QTM upper bound with your code? well, more of a 5thTM I suppose, the QTM equivalent on the Megaminx, that'd be pretty nice also I'm confused, how did you get 116? 10 + 15 + 14 + 8 + 14 + 13 + 17 + 26 = 117, however you originally said the 2nd stage of...

yeah, it was overly long looking back at it, I really want to make sure the reader can follow what I'm doing, plus I wanted to explain the idea at first which took a half or more of the actual OP, going through the simple case of 3x3, presenting the idea of mapping last independent face turns...