Here's the full graph of the game logic (SVG) (spoilers):

https://cdn.rawgit.com/CyberShadow/11329584/raw/5d295c9557d3...

Code: https://gist.github.com/CyberShadow/11329584

Legend:

  - Round nodes are problems
  - Rectangular nodes are things you can have
  - Gray round nodes are problems that don't go away after solving them
  - Green lines are things solving problems gives you
  - Red lines are things needed to solve a problem
  - Dotted black lines are things you need to have for a problem to appear
  - Dotted red lines are problems that disappear when a problem is solved