Engineering Projects/Poppit/Math

There is a relevant theorem to this game called the "Four color map theorem." It says with just four colors of balloons, if the game poppit were randomly generated, there would eventually be an impossible poppit game generated. However, the game may have an internal regulator that eliminates impossible games and only displays those that can have all balloons eventually popped. This would have to be determined through statistical analysis or a program written using this theorem (expanded to 5 colors) that identifies impossible games.

Another thought was to make the game linear by looking at each color sequentially and creating a two dimensional spectral wave from the color pattern. Then something like a two dimensional correlation analysis might be done to see if a strategy for popping all the balloons is revealed.

Perhaps the math of the Traveling salesman problem can be used.