itch.io

I think the puzzle is very clever! I just don't think the accepted answer actually fits the parameters, and I think two other answers do. The point of the puzzle is to deduce the values of the digits from the hints, and you can deduce from hint 5 (together with the promise that the puzzle is solvable) what the fourth digit is and what the other three sum to. With that information, hints 1 and 4 are redundant, and two answers are possible. The accepted answer is only unique and correct (with no redundant hints) if you ignore some of the information hint 5 gives you.

Just to see if I'm clear on the disagreement here: it's about whether or not it's valid to use "there is a unique solution" as part of the constraints?

Because I had started by assuming that since hint 5 is the only thing that constrains digit four, in order to have a unique solution, the first three digits must sum to either eight or zero. And that still seems obviously true to me.

But your position is that "there is a unique solution" is sort of an external check and may not be used as an actual constraint? I can see that if you're not allowed to say "there is a unique solution, therefore the digits must sum to 8," then you're left with "IF the OTHER hints fail to force the digits to sum to 8, THEN you don't have a unique solution." And that makes hints 1 and 4 are NOT redundant in the yes/yes/no case for hints 2/3/5.

Do I have that right?

It still does seem very strange to me that unique solution would not be an allowable constraint when non-redundant hints is. So yeah, seems like a "both reasonings are the other way around" problem, and therefore a poorly-designed puzzle. But hey, game jam.

Ah, dustbunnies. Now I see the error in my logic. It's true that hint 5 says that ifthere is a unique solution, it must have this property. But that doesn't help you answer the question of  whether a particular set of hint answers rules out all of the non-unique answers that may or may not have that property. Gah. OK.