Task $1-2\mathrm{.}5$ points

a$)$ Describe parameters characterizing states in the game given below;

b$)$ Create a game tree for the game described below. Each node of the game tree must contain not only values of parameters characterizing states, but also its label $($A$,$ B$,$ C$,$ etc.$)$ chosen arbitrary by the student.

Game description

A numerical string $"2-1-2-1"$ is given to the players at the beginning of the game and the players' score is $15$:$15.$ During a move, the player sums up a pair of two adjacent numbers and replaces it by the sum result. The sum result is also subtracted from his current score. When only one mumber is left in the string, it is taken and subtracted from the current score by the player who has to make the next move. The game ends when the numerical string is empty. If the score is the same for both players, the result is a draw. If one of the players has a score of $4,$ that player wins the game. Otherwise, the player with the higher score wins the game.