awesome concept
pros: really awesome idea. nice graphics. nice sound. bug-free as far as i can tell.
cons: some major problems with the implementation and some illogical puzzles that have no solution. i'll list below.
the lily jumping puzzle involves some paths that are hamiltonian paths (visit every node at most once) but not eulerian paths (traverse every connection once).
(graph has eulerian route) <-> (graph has at most two nodes connected to an odd amount of nodes)
a quick glance can show that most of the harder puzzles did not have eulerian routes.
it's clear that you generated these mostly randomly with no checking since the larger the graph the more likely it won't have a eulerian route if you don't check for this condition. nice concept and a good way to test intelligence if it was implemented correctly.
here in my opinion is the main problem with the game:
it doesn't have a clear goal. is your goal to roll the highest with the die and reach the end first? or to do better than everyone on the puzzles and have the highest IQ at the end? if it's not a race then why not just have a set amount of puzzles and toss the board out altogether. (or simply make the board such that everyone advances one square per turn)
you could also solve the problem by having the player move X amount of squares forward after their puzzle depending on how well they did.
the IQ thing could just be a value given at the end of the game. there's no point in having it update during the game.
i'm assuming you didn't do this either but if you had the game connect to a central server that had all results of all games played tallied, it could generate a nice normal distribution of scores and results and actually give a real "IQ score."
you have a game here that probably hundreds of thousands of people will play. if everyone's scores were normed against everyone elses.. you'd be able to actually generate a very valid iq score that might even have validity higher than 2 or 3 standard deviations. this would be very interesting.
that last part was just a suggestion and not something i consider a problem.
overall i have to count off because of unsolvable puzzles but this is a very good game that once fixed will be what i consider a "perfect 10."