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Why would it be fancy?
I would assume the hypothesis is that it contains all the numerals 1through to 8 exactly once.
A note with the numerals 1 through to 8, in numerical order, would be a "ladder" and would certainly be worth something. A "jumbled ladder" isn't, sorry. Even a "just-slightly-jumbled-ladder" number like "12435678" wouldn't hold a premium, just like an "Almost Radar" like 12344231 isn't worth a premium either. That's because the number of "almost but not quite fancy" notes greatly exceeds the number of actual fancy notes. It's simply far too common to be "rare", and it's not an obvious-at-first-sight pattern.
Or look at it this way: there is only one way to arrange the digits 1 through 8 to form a ladder (or two, if you include the "reverse ladder")- so finding one is literally a 1 in 100 million chance. But there are eight factorial (8!) or 40,320 different ways to arrange the digits 1 though 8 that aren't ladders.
Yes, it's improbable - 40320 out of 99999999 is a 0.04% chance - but improbability alone does not make a "fancy number". After all, all serial numbers are "unique" and therefore equally improbable. the number "16784253" has exactly the same 1 in 100 million chance as "12345678". But it's not "fancy", because there's no pattern.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis