These are the 'legit' major and minor key signatures. There are zillions of theoretical key signatures and modes that aren't conducive to a key signature. It's my understanding that Bartok would occasionally mix flats and sharps in key signatures (Levine).
In a piece of modal software I am particularly familiar with, the key signatures are really troublesome. (So I can understand the BIAB challenge.) When attempting to describe ALL scales in ALL keys, it becomes apparent pretty quickly that 100% accurate use of accidentals (double sharps, double flats, no repeats of note names) can easily obscure the lessons in intervals, music, repeated patterns and relationships, and the meaning from the largest audience. IMHO.
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