Especially that last one, it poses a question as to whether you can use a grammar to show that a snake lives (doesn't bite itself). Unfortunately she doesn't provide a solution to the problem, but me and a few mates went ahead and proved that it is impossible to prove whether the problem is solvable without simulating the snake.
http://www.youtube.com/watch?v=DK5Z709J2eo (infinite series through doodling)
http://www.youtube.com/watch?v=heKK95DAKms (graph theory awesomeness, through doodling)
http://www.youtube.com/watch?v=e4MSN6IImpI (some lovely properties of binary trees ... through doodling)
http://www.youtube.com/watch?v=Gx5D09s5X6U (snakes)
Especially that last one, it poses a question as to whether you can use a grammar to show that a snake lives (doesn't bite itself). Unfortunately she doesn't provide a solution to the problem, but me and a few mates went ahead and proved that it is impossible to prove whether the problem is solvable without simulating the snake.