Will AI be able to make a new Sudoku ruleset variant, where from it, you can have infinite unique puzzles?
250
resolved Feb 14
Resolved
NO

I am not looking for an infinite number of sudoku rule variants but A sudoku rule variant that if following the ruleset, if we asked the AI to produce more puzzles IN that ruleset, would it be able to generate infinitely many unique puzzles that can't be solved simply by human generalized techniques?

Criteria: (This market resolves in a month because i want to track the process of these developments month by month.)

1) The puzzle board can't be infinite and neither can the amount of numbers involved in terms of the ones you write down or the ones that exist already filled out on the board. By general human technique I mean any pattern that a human can pick up on in general and solve more puzzles with it based on a pattern from the rules and patterns in it's implications, like those used to simplify solving traditional sudoku puzzles. It's kind of like asking can an AI generate, when prompted, an infinite amount of unique games without a human getting wise by looking through some and making a generalized technique that makes the puzzles non-unique to solve and at some time in it generating puzzles a pattern to solve some, most or all is discovered.

2) Resolves YES if an AI can generate a sudoku variant where nobody who contributes to this market and any primary sources involving this AI, can spot a pattern and where they can easily keep generating sudoku puzzles, based on how they are generated, solve them that way rather than directly playing through them. It is my understanding traditional sudoku although vast in diversity can be solved regardless through generalized techniques. I’m asking if an AI can create A sudoku variant (a sudoku variant with a new ruleset) in which no generalized technique is possible across puzzles that are based on that ruleset, no matter how many puzzles it generates (infinitely) Will never resolve N/A, resolves NO if no evidence is shown that these developments are happening or if someone shows that it's impossible for such a sudoku variant to exist or that an AI cannot do this.

(Updated Jan. 7 in hopes of making it clearer. If changes changes the nature of the market to you, i will be willing to give you your mana back. Changed the phrasing of the question and the description)

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>The puzzle board can't be infinite and neither can the amount of numbers involved in terms of the ones you write down or the ones that exist already filled out on the board

Just to be clear, the puzzle board can still be arbitrarily large, right? Otherwise the answer is trivially NO (there are only finitely many puzzles of any given finite size).

>It is my understanding traditional sudoku although vast in diversity can be solved regardless through generalized techniques

If you allow the board to be arbitrarily large, then not really. Sudoku (on a board of arbitrary size) is known to be NP-complete, so it is believed to be computationally unfeasible if you make the puzzle large enough. This means the answer should trivially be YES (unless it is trivially NO, as per the above): just generate regular (big) sudoku puzzles, no variation nor AI needed.

@Mira I'd be shocked if you didn't have an opinion on this.

bought Ṁ5 of YES

I previously bet NO on this, but I came back to it just now, and isn't this already possible with hand-coded software? Say https://sudokutodo.com/generator. Or does that not count as "AI" and you were expecting something like ChatGPT to be the one writing the Sudoku puzzles?

When it comes down to it, all Sudoku puzzles are very similar to each other, and they're all pretty much solvable with the same human techniques... if you were asking about AI inventing new games entirely, each completely novel and requiring different strategies, that would be more interesting to me, but I'm not sure how to operationalize that as a market with well-defined resolution criteria

@CDBiddulph This is my attempt to operationalize such a market in real time. The well-defined resolution I think is implied in the comment I tagged you in below but to try to be absolutely clear: Resolves YES if a AI can generate a sudoku variant where if it can generate infinite puzzles based on that variant no generalizable technique to solve across them for humans exists. With this in mind I’ll edit the description and try to make the contours more clear with the phrasing. Sudokutodo, the link you said, would count but i'd have to look into whether or not it can truly generate infinitely many unique puzzles that no human generalized technique can solve. I'd assume the consensus is no. Will find evidence in your favor or against and post it here.

@ThePhilosopher Description updated, any comment on whether things are more clear in terms of well-defined resolution criteria let me know one way or another :)

predicted YES

@ThePhilosopher I mean, this seems more like a question about Sudoku itself rather than about the capabilities of any future AIs. I think Sudoku is just a simple enough game that it's straightforwardly the case that all solvable Sudoku puzzles can be solved by humans with a "generalizable technique."

The simplest generalizable technique is to choose every possible number in each empty square in a depth-first search until you happen to get the correct solution. You can make that technique much more efficient by adding in more strategies like this (just the first Google result for "sudoku strategies").

By "AI inventing new games entirely," I meant inventing rules for completely new games, like if it saw Sudoku in its training data and then invented the concept of nonograms, Futoshiki or Kakuro

@CDBiddulph This is what i'm referring to when saying Sudoku variant, hence "AI inventing new games entirely" The link you sent, i'm not familiar with those variants and that's why i thought it may be possible that it may just be about sudoku if there are ALREADY sudoku variants like this, then an AI doing it wouldn't matter to me.

predicted YES

@ThePhilosopher Aaah okay, yeah I was confused. I think I read "jumbo Sudoku book" and got locked into the idea that the AI was generating Sudoku puzzles and not "games similar to Sudoku." You used the word "variant" later on, to be fair

Still, with this in mind, generating an "infinite" number of Sudoku rule variants that are solvable by humans as you write in your question would be theoretically impossible. "Infinite" unique variants is very different from say, one million of them. Here's why: if we suppose unlimited Sudoku variants exist and the AI gives them to you in order from simplest to most complex, the rulesets will eventually become too complex for any human to comprehend. This puts a lower bound on the number of human-solvable Sudoku variants an AI can invent.

@CDBiddulph I'm convinced my phrasing is fundamentally incoherent so i shall be trying again to make things clear. I agree with you completely here but i am not looking for an infinite number of sudoku rule variants but A sudoku rule variant that if following the ruleset, if we asked the AI to produce more puzzles IN that ruleset, would it be able to generate infinitely many unique puzzles that can't be solved simply by human generalized techniques?

bought Ṁ20 of NO

@ThePhilosopher Okay, creating infinite unique puzzles is also impossible, for pretty much the same reason. You specifically said that the board itself shouldn't be infinite, but any ruleset where the initial board is specifiable in a finite number of bits necessarily has a finite number of possible boards.

Concretely, Sudoku has at most 10^81 possible initial boards (81 squares, where each square can be one of 9 numbers + 1 blank). Of course, 10^81 is finite, so no one can generate infinite unique boards. You can make the same argument for any game with a finite board size.

bought Ṁ100 of NO

@ThePhilosopher It feels like you need a way clearer resolving condition. You seem to have a vague mental idea in mind. But throwing out the word "infinity" does not a criterion make. Much less a fair market problem

An example of a less unfair market problem will be.
- On Feb 6, a "general purpose AI" (not a sudoku writing software) of my choice will generate 30 9x9 sudoku with variant rules. Every sudoku can have standard rules or one of the ~50 rulesets/constraints written on https://logicmastersindia.com/forum/forums/thread-view.asp?start=1&tid=777

- If at least 90% of the sudokus have (a unique solution AND they feel "not machine generated and dull" to me) then this resolves to YES.

-Else this resolves to NO

You cant track month to month advancements in AI by setting goals mathematically impossible like "infinite variants" forget the rest of it

When does this close? Today? This year? 10 years later?

Who decides if the puzzles are similar enough?

I cant tell if you're asking with a thing in mind, or just trying to get a bunch of AI generated sudoku puzzles

@Soni I apologize for the confusion as to the date the market expires. Not sure how it didn’t even have one. It is now Feb. 6 as this market is more to test the waters on the month by month advancements of such a possibility in real time, resolves YES if an AI can generate a sudoku variant where nobody who contributes to this market and any primary sources from this AI are given on where nobody can spot a pattern where they can easily keep generating sudoku puzzles and based on how they are generated solve them that way rather than directly playing through them. It is my understanding traditional sudoku although vast in diversity can be solved regardless through generalized techniques. I’m asking if an AI can create a variant in which no generalized technique is possible across puzzles, no matter how many puzzles it generates (infinitely) @CDBiddulph

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