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The winner's score appears to be a mix of how many turns it takes to ultimately propose the correct solution and then a sort of multiplier is applied based on the game situation (AI difficulty). The top score I've gotten in a solo game is 480 points, which IIRC was a full match of hard AIs and then getting the correct solution within 2-3 turns. Being honest, while it's nice to go for a "record", I think the points skew things too far into the area of luck being a primary contributor. I don't put much weight in them myself, though could be useful in friendly top score sparring. I also don't know of a better approach to scoring that could be programmed and standardized.
As for the leaderboards, scores between matches add up in that context, remaining live during the course of the week and then get reset each Sunday. Last week I think my offline leaderboard score was in the area of 1200 points, but those were from something like 6 matches I won (along with 3-5 losses that gave no points). I don't often play online matches, but as I recall losing one there grants 50 points in consolation.
Lastly, for full clarification, using the hints feature in an offline match will block points entirely, which I do agree with. Hints should only be used by very very new players or actual children just wanting to have a fun experience.