In post 1452, Farren wrote:I'd object to that, because it would imply that I'd have to understand what's going on too, and my understanding of the meta-rule isn't as firm as I'd like.
Like, take your bingo. Numbers containing a 1. I can turn that into a meta-rule: "Numbers containing a specific single digit." But I'm not sure where exactly the dividing line is between "cases where there's a meta-rule" and "cases where there isn't."
I also have no idea how to prove that a given bingo falls foul (or doesn't) of the meta-rule clause; all I know how to do is experimental "proof" (generate hands of numbers and see how many are a match - which proves nothing; if you flip a coin three times and it comes up heads three times, that doesn't prove the coin's rigged). And I can't do that very fast with my current understanding of spreadsheets, so trying to do it 64 times is a major headache.
The simpler the bingo is, the more likely it fits the rules. For example "all the cards are even" or "is divisible by 3 with 1 left over" are acceptable bingos, and the meta rule in this case is "Are any of my cards divisible by 2? Divisible by 2 with 1 left over? Divisible by 3? Divisible by 3 with 1 left over? Divisible by 3 with 2 left over? Divisible by 5? ..."
If your method of generating bingos is "glance at my hand and notice something really obvious, like all of the numbers are prime" then that's always going to be allowed as long as less than half of the numbers below 100 have this property. (nonprime by itself is way more than 50 so that wouldn't work).
If you're playing without a spreadsheet, then you will never run afoul of the meta rule.
but if you're curious, the way you work out it without trying all the options is through a branch of mathematics called Combinatorics. It's pretty fun, especially early on when the problems are less hairy, but it's also pretty easy to make mistakes and real life combinatorics problems can get pretty ugly