How to solve the ASTROLABACUS™ puzzle (four-colour configuration)

This guide outlines a general strategy for the ASTROLABACUS™ puzzle in the four-colour configuration. The same approach extends to other colour configurations with minor adjustments.

This is not an exhaustive tutorial; it covers the essential moves and sequences required to solve the puzzle.

Note: the accompanying video contains some handling noise; captions/subtitles are provided.

No advanced algorithms are required. Once familiar with the puzzle’s spatial articulation, the solution is straightforward.

The algorithms are written below in case they can be useful to someone else, but they look way harder written than they really are put in practice. I am assuming one is holding Astrolabacus in position B2 shown in Link. Other definitions may not necessarily be the same as in that website.

Definitions
S-shift balls clockwise by one position
T-lift top right segment up (red segment)
Segment-piece containing two channels, six balls
Channel-single piece containing three balls

Algorithms
(nS)T(nS’)T’
-if n=1 permutation involving third ball on the top left channel (green/orange pair) and the six balls on the top right segment (red channels)
-if n=2 permutation involving second and third balls from top left channel (green/orange pairs) and the six on the top right segment (red channels)
-if n=3 permutation of top left channel (green/orange) with the two channels from the top right segment (red/green and red/orange)
-if n=9 top right (red) and bottom left (green-orange) channels ball swap
(Note: symmetric movements always occur on bottom right and left channels whilst solving)

2S[T S T’ S’] [T S’ T’S’]
swap left ball on bottom left channel (orange/red pair) with the second ball on the bottom left channel (green/red pair). This also swaps other two pairs of balls (first and second balls on top left channel - green/orange pair, and second ball on top right channel - red/green pair with third ball on top right channel - red/orange pair), check video for more details.

Nothing else is required to solve the puzzle. In any case, for the particular case shown in the end, one can write the overall algorithm like follows, but is easier to do it intuitively as explained in the video. 3S 2T [T’ 3S’ T 3S] [T 3S T’ 3S’] 2T’ [3S’ T’ 3S T]

General procedure
1-Solve blue/green pair
2-Solve blue/orange pair
3-Solve blue/red pair

No particular algorithm is needed up to this point. For the next steps, combinations of (nS)T(nS’)T’ are needed to achieve the goal. Always keeping the blue channels solved, unless otherwise stated. Typically n=1 and n=9 are the most commonly used combinations.

4-Place all red balls on the top right segment (red) and check how many balls on the top left channel (green/orange pair) need to be flipped
5-If one or three balls on green/orange pairs need to be flipped then shift balls 3 positions clockwise and quickly solve the blue channels from step one
6-Finish the top left channel (green/orange). May need to flip two orange balls
7-Sort bottom left segment (green/red and orange/red pairs). This can be done by doing set-up moves with (nS)T(nS’)T’ (n=1) then applying 2S[T S T’ S’] [T S’ T’S’] to typically swap the left ball on the bottom left channel (orange/red pair) with the second ball on the bottom left channel (green/red pair)