Thanks makes more sense! Idk why the downvotes… Because in the case of an offset it would always be wrong and in the case of a speed change.

In the general case, with clock speed a and offset b: a x + b ≡ x (mod 12) a x + b = x + 12k

If a=1, normal speed with offset, b = 12k ≡ 0 (mod 12) So it works for any multiple of 12h offset (ie no offset)

If a≠1, x = (12k - b)/(a-1) isn’t always in a day, so you can end up having to wait multiple days for it to be right