I once pondered about a much stronger version of this problem, where not only you don't know which segments are faulty, but also you can't tell one state from the next state that is identical to the previous (i.e. no forward button, nor known update interval), and you don't know which variant glyphs for some digits are used. I was partly motivated by digital clocks in a bus, which I could never continuously observe, explains those changes. Obviously they had a great impact on the number of possible states---somewhere around ~100K states---and my attempt to draw a reasonable graph out of them was futile.