KöMaL 2007 K111

In a game, two dice are rolled and there are 9 cards numbered 1 to 9. The total of the numbers rolled is to be put together as a sum of number cards (or a single card). Each card can only be used once. Used cards are set aside and the sum of the next two numbers rolled is put together out of the remaining cards. And so on while it is possible. $a$) What is the minimum number of rolls may in a sequence of rolls where all number cards are used up? Give an example, too. $b$) In the worst case, what is the smallest number of rolls that may end the game?