Task $5$

a$)$Define parameters characterizing state in the game given below

b$)$Create a game tree for the game given below

Game description:

At the beginning of the game, the number $216$ is given to the players. Each player has $4$ points. Theplayers alternate moves by dividing the current number by $2$ or $3.$ It is possible to divide the number onlyif the result is an integer. If the number obtained after the division is an even number, then $1$ point issubtracted from the player's score. However, if the number obtained is an odd number, then $1$ point isadded to the player's score. The game ends when the number $2$ or $3$ is obtained. The player who has thehigher score wins the game.

While doing please also take into account belowed rules:

$1.$Each node should represent values of all parameters characterizing states in the game together with student$$s given unique label like A$1,$ A$2,$ etc.

$2.$All arcs must be directed

$3.$No arcs between nodes at the same level

$4.$No arcs crossing several levels

$5.$No identical nodes at the same level