4. Losing Marbles Two EECSTU 081s are playing a game, where there is an um that contains some number of red marbles (R), green marbles (G), and blue marbles (B). 'There is also an innite supply of marbles outside the urn. When it is a player's turn, the player may either: (i) Remove one red marble from the um, and add 3 green marbles. {ii} Remove two green marbles from the urn, and add 1' blue marbles. (iii) Remove one blue marble from the urn. These are the only legal moves. The last player that can make a legal move wins. We play optimally, of oourse meaning we always play one of the best possible legal moves. {a} Prove by induction that, if the urn initially contains a nite number of marbles at the start of the game, then the game will end after a nite number of moves. (b) If the urn contains 2 green marbles and B blue marbles initially, then who will win the game? Prove it. In this case, does it matter what strategy the players use? {(2) If the urn contains {53, (3,3) red, green, and blue marbles initially, then who will win the game? Prove it. In this case, does it matter what strategy the players use