Background Christiane and Matthias are playing a new game, the Number Game. The rules of the Number Game are: Christian and Matthias take turns in choosing integer numbers greater than or equal to 2. The following rules restrict the set of numbers which may be chosen: R1 A number which has already been chosen by one of the players or a multiple of such a number cannot be chosen. (A number z is a multiple of a number y if z can be written as y * x and x is a positive integer.) R2 A sum of two such multiples cannot be chosen either. R3 For simplicity, a number which is greater than 20 cannot be chosen either. This enables a lot more NPCs (Non-Personal-Computers) to play this game. The player who cannot choose any number anymore looses the Number Game. Here is an example: Matthias starts by choosing 4. Then Christiane is no
