[This is a cross-post from Speedsolving Forum: 3920 Notation]

So the conversation in Converting Algorithms to Letters, particularly abunickabhi’s explanation of his “Yo Notation” as well as his subsequent elaboration on memory techniques, led me to have this idea. Yo Notation is probably better (I know abunickabhi has put a lot of thought into it and he has much more experience in this type of thing than me (that’s an understatement)), but I think there’s an interesting idea here as well. The main goal is to artificially reduce the incidence of repeat images by using a pseudo-hash-function.

Note: This is NOT the system I mentioned in that same thread which I have been working on for around a year or so off and on (and may just be worse than what I’m about to outline below despite having taken far, far longer, ironically). I just had the idea for this system a few days ago while reading the linked thread.

28^2 move pairs (6 faces, 3 slices, 3 moves each, plus a null move = 28), each move pair has 5 unique associated images, giving 3920 ( = 5 (28^2) ) total images.

In each new room/station (larger subdivision than a locus, finer subdivision than a palace), find “n”:

- Initial “n” for the first locus and image in a new room/station (where “r” is the room/station number starting from 1 for the first room/station in the palace): “n = (r mod 5) + 1”.
- Calculating “n” after each image (not just after each locus, after every, single, image) in a given room/station:
- Set “n = n + 1”
- If “n > 5”, Set “n = 1”
- Terminate Algorithm. “n” is the new “n”.

Every time a new image is needed, use the nth image of the relevant letter pair. Don’t forget to run the n-updating algorithm immediately afterwards (unless n is reset by moving to a new room/location, of course).

Denote wide moves by doubling the relevant face and direction. (r = RR, u’ = U’U’, l2 = L2L2s, etc.)

Denote rotations by doubling the corresponding slice move. (y = EE, x’ = MM, x = M’M’, z2 = S2S2, etc.)