I must correct rule 2: I am looking for the complete set of unordered 4-tuples, either four identical or four consecutive. Four consecutive is any true 4-substring of ADEFGMSTV.

Sometimes it is not advisable to form a sameness-tuple

I will explain on a minimal example. Split up the set AADDDEEEEFFFFGGM. It is tempting to first take out the 4 same E and F, but then the remainder is AADDDGGMM from which a solution cannot be formed any more because they are not alphabetic neighbours. It is false to give up now and assume that aforementioned set has no solution as there *is* a (single) solution: ADEF;ADEF;DEFG;EFGM. So one has to be smart what to pick first to not end up in dead ends.

Rarely there are multiple solutions, but they do occur. Trivial example is GGGGMMMMSSSSTTTT. Its two solutions are GGGG;MMMM;SSSS;TTTT and GMST;GMST;GMST;GMST.