From the developer point of view I find this interesting.
But from a players point of view it is not that interesting: As a player I do not care about the mathematics, I just run around, collect what I can and expect that everything is "solvable". I do not care how the develper achieved that it is always solvable.
I think you have an interesting alorithm you can build upon. But for the game to be really interesting to play I think you have to add a bit more. What you could try is to add several minigames to make the journey more interesting. Ideas are:
- Replace the signs by NPC that have to be persuaded to provide the information
- Make fights interesting