Vapn wrote: ↑29 August 2023, 00:19
As I said above, I know what people are doing. Or at least I know how this could be done, answering with no questions asked.
Someone, without using a "solver," walk through the logic of this set of verifiers and tell me how you deduce the code without asking a single question.
A: Blue < 3 | Blue = 3 | Blue > 3
B: Blue < Yellow | Blue = Yellow | Blue > Yellow
C: Blue < Yellow & Purple | Yellow < Blue & Purple | Purple < Blue & Yellow
D: Even > Odd | Even < Odd
BIG EDIT: I'm pretty sure this is a 50/50, not an unambiguous solve. I still haven't run it through a solver to prove it, though.
I'll take a swing at this. Note that I'm doing it live, so apologies if it's a little rambly.
First, we can eliminate
Blue = Yellow as a possibility. If it's a criteria, and
Blue = 3, then verifier D is pointless. Both other choices for criteria A require criteria C to be
Purple < BY (since neither Blue nor Yellow can be "the least"); if
Blue < 3 then that forces 221 and verifier D is unnecessary, and if
Blue > 3 then the solution is ambiguous, as 44x and 55x both force criteria D but provide no clue as to what value Purple has.
Now, consider
Blue > 3. If
Blue > Yellow, we again enter the realm of foggy ambiguity. Neither
Purple < BY nor
Yellow < BP provide nearly enough constraints on the values, as Blue is in {4, 5} and Yellow and Purple are swimming around in, at minimum, {1, 2, 3}, allowing for any mix of evens and odds verifier D could ask us for.
If
Blue < Yellow, then we have 45x. If
Blue < YP, then it's 455 and D is again unnecessary. So if it's anything it's
Purple < BY. There are two odd numbers less than 4, but only one even number, so D would have to be
Even > Odd and the answer is
452.
OK, that's great, so we need to prove now that it can't be
Blue < 3. If it is, and
Blue > Yellow, then it's 21x and we have to set C to
Yellow < BP. But either choice for D is ambiguous, since purple can be any of {2, 3, 4, 5}, leaving it two choices whether there are more even or odd numbers. So nope. Our last option is
Blue < Yellow. Let's go through the three options for C now:
- Blue < YP: Blue is {1, 2}, and Yellow and Purple are {2, 3, 4, 5} or {3, 4, 5} depending on Blue. Neither of the choices for D can possibly disambiguate this, as there are simply too many options.
- Yellow < BP: Literally impossible, since we already chose Blue < Yellow.
- Purple < BY: We have 2x1. Yellow can be {3, 4, 5}, so we have to pick Even > Odd as the choice, so that the result can be 241 rather than the ambiguous odd choices.
So it seems like the answer can be either
452 or
241, and it all hinges on whether
Blue < 3 or
Blue > 3 (since both of them end up with the same values for the other three criteria). That's a 50/50, though, so I could see someone taking a swing at it with zero verifiers. It's also possible they just didn't see the second alternative and thought there was only one option--as I did the first time I wrote this out--and got lucky.
P