Only 2 tries in Arena? Could someone explain this game?

[ShiroC4t]

Table No. = 469554670

How could we know the answer in 2 tries? Could someone explain to me, please?

[poptasticboy]

So I haven't worked through this specific puzzle, but I can give you some general tips that are used to deduce the results of verifiers without needing to test them. Sometimes you can even solve certain puzzles without using any tests at all!

It's important to understand these two basic tools:
1) No verifier can be redundant.
2) There must be a unique solution.

Rule 1 means that every verifier must be necessary to find the solution. If any response or set of responses from verifiers would mean that another verifier no longer gives you any additional information, then that set of responses is not a valid combination.
Furthermore, if you think you have a possible solution, but removing any one of the verifiers would still lead you to the same unique solution, then that solution can not be the correct one.

A very simple example from a quick glance at this puzzle would be: F can not be verifying "Yellow=3" because then you would already know that Yellow is Odd, making A redundant.

Rule 2 means that if a particular combination of responses leads either to zero codes or to more than one code, then that combination can not be correct; only combinations of responses that lead to exactly one solution are valid.

It is also important to understand how the verifiers work, in particular in relation to the non-exclusive criteria cards (26–48). Each verifier knows that one of the criteria listed on its criteria card is true. However, it knows nothing about the other listed criteria; they may independently be true or false, but they will have no bearing on the responses that this verifier gives. The verifier will simply respond if your code obeys the one fact that it knows and if your code does not obey it; the other listed criteria are irrelevant. Your job is to work out which one fact it knows.

For example, I said earlier that F "can not be verifying Yellow=3". I chose the wording carefully; I did not say that Yellow can not be 3; merely that F can not *know* that. If F happens to be verifying a different colour in this puzzle, it will know nothing about Yellow.

If you'd like an example of a Hard/6 puzzle solved in 0 tests, I posted a solution to a puzzle here:

https://boardgamearena.com/forum/viewtopic.php?t=34642

[Jellby]

For reference, the link is: https://boardgamearena.com/table?table=469554670
And the criteria cards are:

A: (6) Y is even | Y is odd
B: (18) B+Y+P is even | B+Y+P is odd
C: (24) ascending sequence of 3 numbers | ascending sequence of two numbers | no ascending sequence
D: (32) B > 3 | Y > 3 | P > 3
E: (36) B+Y+P is a multiple of 3 | B+Y+P is a multiple of 4 | B+Y+P a multiple 5
F: (40) B < 3 | B = 3 | B > 3 | Y < 3 | Y = 3 | Y > 3 | P < 3 | P = 3 | P > 3

What I can say is that after those two questions, that is the only possible solution. There's still ambiguity in whether D and F are "Y > 3" and "P > 3", or "P > 3" and "Y > 3", but that obviously doesn't change the answer, which is the same in both cases. If any of the answers had been different, 2 questions might not have been enough.

Using poptasticboy's rules, you may easily rule out "B+Y+P is a multiple of 4" because card B would be redundant in that case. You can also rule out "ascending sequence of 3 numbers" in all problems, there are only 3 codes that satisfy it (123, 234, 345), so it could only be valid in a 4-card problem, but even then it's not interesting enough (I guess) and the card does not exist. With that, there are only 432 possible verifier combinations to test by brute force

[poptasticboy]

For reference, the link is: https://boardgamearena.com/table?table=469667686

That's the wrong table number in Jellby's link, it's actually https://boardgamearena.com/table?table=469554670

[Jellby]

Indeed, sorry, fixed now.