Find the Grundy number of the initial position and make the first move in a winning strategy for the following game:
In a pile there are two red balls, four green balls, four blue balls, and six white balls. A player can take a (non-zero) number of balls of same color: one red, or one or two green, or one, two, or three blue, or up to four white balls.
How do I do this? I've only ever done Nim games with multiple piles; never have I had one pile with multiple types of objects in one pile.