On the Subject of Wire Sequences
JavaScript (ES6), 75 74 67 bytes
Expects a list of [color, label] pairs, using 0-2 for both. Returns a binary array describing which wires must be cut.
a=>a.map(([c,w])=>(m[c]/=8)>>w&1,m=[334844576,228136272,611931512])
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63 bytes
We can save a few bytes by taking A=1, B=2, C=4 and returning a list of zero / non-zero values.
a=>a.map(([c,w])=>w&=m[c]/=8,m=[334844576,228136272,611931512])
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How?
Each color is encoded as a bit mask describing the wire labels for the 1st to the 9th appearance.
# | 9 8 7 6 5 4 3 2 1 (0)
Label | CBA CBA CBA CBA CBA CBA CBA CBA CBA ---
-------+-----------------------------------------
Red | 010 011 111 101 010 101 001 010 100 000 -> 334844576
Blue | 001 101 100 110 010 001 010 101 010 000 -> 228136272
Black | 100 100 011 110 010 101 010 101 111 000 -> 611931512
Whenever a color appears, we right-shift the corresponding bit mask by 3 positions (by dividing it by 8) and we test the bit 0, 1 or 2 according to the label.
Retina 0.8.2, 119 bytes
s`(\d)(?<=(\1.*?)+)
$1$#2
%`(23|4|26|19)A|(22|1[136]|03|5|06|29)B|(2[148]|04|6|17|09)C|(07|28)[AB]|([10]2|18)[AC]|01|27
Try it online! Takes input as list of digit + letter pairs where the digit is 2 for Red, 1 for Blue and 0 for Black. Output is a list of whether each wire should be cut. Explanation:
s`(\d)(?<=(\1.*?)+)
$1$#2
After each digit insert its cumulative appearance count.
%`(23|4|26|19)A|(22|1[136]|03|5|06|29)B|(2[148]|04|6|17|09)C|(07|28)[AB]|([10]2|18)[AC]|01|27
For each wire check whether it needs to be cut.
Rust, 89 bytes
|w|w.scan([0;3],|a,&(c,l)|{a[c]+=1;Some(b"TGjEQBMERBuFgCkDJD"[2*a[c]-2+c/2]>>c%2*3+l&1)})
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Explanation:
Both colors and labels are encoded as numbers from 0-2. The output is a number for every wire: 1 if it should be cut, 0 otherwise. The b"TG...D" string contains a binary encoding of the above table. The labels to be cut in every cell is transformed into a 3-bit mask. Three of these masks can be packed into two bytes (Red and Blue in the first byte and Black in the second byte). The 6-th bit (which is unused) is also set, to make all the characters ASCII printable (to not need escape sequences or raw strings).