@freemo that's exactly why I asked you :)

@freemo but maybe I can use it to have a reasonable language to start generating the fact templates.

@freemo let me think about it that way...

See if I can come up with something.

@freemo well, sort of. But you still have clues that are still relative. For example

abc

def

ghi

A is left of b, c

A is also left of e, f

A is also left of h, i

So Bob is left of Charlie, but another clue is Bob is left of The person who smokes Pall Malls. Or the person who has a Zebra, and so on...

These have multi-dimentional inferences in that way. I get that. But I have to start my thought process somewhere. So reducing it to 3x3 and ABC is a good starting point, from which to build up a theory. No?

@freemo Just thinking out loud. in a 3x3, a "left of" eliminates 1 position. 2 of them would infer that rightmost position as the one not referenced. Though there would be some other clue necessary to determine their specific location:

A is left of C

B is left of C

Infers C is rightmost. But doesn't solve AB vs BA

A is left of B

B is left of C

Infers C is rightmost

Infers A is leftmost

Infers B is in the middle

So 2 relative rules that commonly refer to a given element, infer that element, but not the relative ones. But 2 relative rules that do not share a common element will infer all 3 elements.

This is intuitive to me, but I don't know how to define that.. Or scale it.

@freemo but I was hoping rather than a solver, a mathematical proof.

Seems like a given rule either infers or eliminates relationships, and enough of such things would in theory present a solveable set. No?

@freemo well, I think there is something to generating all possible clues.

Within any given column there is a direct positive and or set of negative clues relative to every other elements in that same column.

And for any element in any column will have positive and negative relationships either "left of" "right of" "next to" or possibly "between" (which would be relative to two other column values.)

@freemo Just wrote a program that presents such a problem. Due to time constraints we wrote it for 3x3 rather than 5x5 or whatever it normally is. But I wrote the clues manually, as I proved them out, and resolved the puzzle myself. I came up with 5 templated sets of rules and then we shuffle different entities and attributes through the puzzle. But I am considering expanding it to the full size puzzle at some point, and assume there should be some straight forward way to create all the "facts" relationships etc.. To come up with rule sets.

One explanation was to come up with all the possible "facts" (since they are definitely finite) then somehow determine that some number of them would be sufficient to solve it. Or something like that.

@kat was that MapMyWalk?

:)