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Comment by abrax3141 | Hacker News Reader

Fun implementation. It’s isomorphic to a wide range of problems that have been used for centuries that are all isomorphic to constrained state search. The fact that the graph is explicit here makes the problem way easier. (One you may be familiar with that seems very similar is the parking problem where by sliding around the cars they (un)block one another. None of this is to take away from the fun setting and implementation. Just that it’s not a new type of problem, although it seems to be a fun new instance of a common type of problem.

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I would argue that the visual presentation and interface is a big part of what makes a puzzle, and changes how it is perceived, and therefore it is a new type of puzzle.

Fair enough. Depends how you arrange your ontology. But then anything is a new type of problem, so the claim becomes meaningless.

When you're solving the sliding cars puzzle as a person you're not thinking of graphs. The experience of solving OP's puzzle is entirely different from the one you mention. In theory you could stop, write down the underlying graph representation and solve it that way I suppose. Does anyone do that though?

You’re correct. (As I mentioned, having the explicit graph makes it easier, and as another person mentioned, this makes it an essentially different problem.) I wasn’t meaning to say that it’s identical. Just the closest thing I could think of offhand. When I was in grad school working on problem solving we used to make up new problems every day. Every little change changes the problem’s affordances, but if you define a problem type by the method of solution, all of this class are isomorphic (along that dimension). Again, none of this is to take away from the fun design of this problem.

Code Master is another that, again isn’t identical to this OP’s, but has the explicit constrained ATN. https://www.codewizardshq.com/coding-games-for-kids/

I think your ontology encompasses too much to be useful in classifying games. All single player games without a random element can be modeled as graph search problems with varying degrees of cycles permitted.

Although I agree (mostly- there may be some further structure in my ontology, but not worth arguing about- I’ll buy your characterization), I think that this is exactly what makes it useful.

Woah! Woah! Easy now. We don't need lumpers and splitters shedding blood here.

But are we really lumpers and splitters? And is it blood or plasma? And are we actually shedding it? And who are we anyway?

The graph drawn here is different from the graph of states: the latter has the cube of the number of these graph nodes, and several edges per node, and would be difficult to draw clearly on a flat paper.

The state I’m referring to is is the whole puzzle state. It’s a confusing term in this case.

Yes, and as I said, the number of puzzle states is the number of nodes in the pictured graph, cubed. There is some relation between the two graphs, but they aren’t the same, and the pictured graph doesn’t necessarily show too clearly how to navigate around between different regions of the graph of game states.

Yes. That’s right. In problem analysis the problem state graph is implicit (or virtual, I’m not sure which is the appropriate term). It happen Ms that this puzzle also has a graph, but (agreeing with you) that’s not the psg. We could call the puzzle’s graph the “map” to be a bit less confusing, assuming we want to bother continuing this thread, but I’m guessing that it’s just you and me at this point, and we agree, so we should stop.

is there a branch of mathematics that formally models this isomorphic forms of this stuff? topology? or just plain old graph theory

Hmmm. We’ll, in CS it’s problem solving: https://www.pearsonhighered.com/assets/samplechapter/0/1/3/6...

You’d think that it would be part of game theory, but all the game theory I’ve seen deals with multiplayer games, but it seems like a cooperative total information n-player game is essentially the same as a one player puzzle. So maybe g.t. generalizes in this way.

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