Grade 8 Piano. Chromatic Scales in minor thirds: legato, hands separately: 2 octaves. Beginning on A sharp and C sharp (page 13 in the grade 8 scale book).

I’m trying to find the logic behind the fingering for the above. Can somebody suggest something useful? I can see certain groups of three but no other guiding pattern to help memorising this scale.
Any suggestions would be appreciated.
FGP

Depends which fingering you prefer but if you use the first suggestion I found that knowing which pairs of notes in each hand are played with 3/5 in each octave helped me.

By the time you've repeated them a few hundred times you'll never be able to forget the fingerings. Somewhere along the way the logic of them will dawn on you.

When I did my grade 8 today my examiner introduced this by saying 'and now for the nightmare scale'. Perhaps even examiners can't see the logic behind it.