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How to approach a capture solver with pathfinding and optimization?

i´m a first year CS student, trying to solve the following game in Java.
SS of game
Rules:
1.) The player and computer take turns. The player starts. Before the game 14 random Hexagons get deleted.
2.) The player can delete one Hexagon on each of his turns.
3.) On his turn the computer moves one hexagon from his current position. The priority of the computers movements is known to the player.
4.) The game ends when either 10 turns are over, or the player has deleted all edge hexagons the computer can reach. The computer wins if he reaches an edge Hexagon or an edge Hexagon is reachable after ten moves. Otherwise the player wins and gets score depending on how many hexagons the computer is locked in on.