@freemo Other than manually, is there a mathematical way to calculate the "clues" for the "Einstein" or "5 houses" style puzzle?
It seem like you'll need the holy grail:
https://www.youtube.com/watch?v=lWHN5WXMFHc
It's a solution to a more general problem by boiling it down to linear algebra, using Zhegalkin polynomials. The process itself is rather straight forward, with the added bonus that each step more or less fully represents the problem, there is very little reduction going on, so makes it easier to think about how it can be reversed. Not trivial though, in particular there is a combinatorial explosion going on (though it adheres to a certain pattern, so might only be "apparent explosion"), and of course there is the challenge of converting the polynomials to some interesting/natural prepositional logic statements, for which you'd probably have to go with some rigid structures and vary certain mostly irrelevant components (trivial example would be using the classic and/or/not operations and just swapping the variables). Unfortunately most of the work in this area that I'm aware of is aimed at finding minimal rather than interesting representations. Very hard to imagine how you would go from a set of polynomials to a high level concept like ordering of houses, but just another perspective, and if nothing else a simpler example to think on.
