Refer to image attached! 2. Euclid's Game starts with two unequal positive numbers on the board. For this problem,assume that permissible starting numbers are in the range [1, 50]. Two players move inturn. On each move, a player has to write on the board a positive number equal to thedifference of two numbers already on the board; this number must be different fromall the numbers already written on the board. The player who cannot move loses thegame.a. Give three examples of a 'game tree' for Euclid's Game for any pair of numbersyou choose.b.Should you choose to move first or second in this game?

As described in the question the Euclid's game is a strategy oriented game. The key to winning this game is understanding the concept of the greatest common divisor (GCD). If one plays optimally and calculate the GCD at each step, they can ensure victory.part a) Three Examples of Game Trees for Euclid's GamePair: (8, 12)1 (8, 12) 2 / | \ 3 (4, 8) (4, 12) (8, 4) 4 / \ / \ / \ 5(4, 4) (0, 8) (4, 0) (4, 4) 6 / \ 7 (0, 4) (0, 4) 8Pair: (15, 25)1 (15, 25) 2 / | \ 3 (10, 15) (10, 25) (15, 10) 4 / \ / \ / \ 5(5, 10) (5, 15) (10, 5) (5, 5) 6 / \ 7 (0, 5) (0, 5) 8Pair: (20, 30)1 (20, 30) 2 / | \ 3 (10, 20) (10, 30) (20, 10) 4 / \ / \ / \ 5(10, 10) (0, 20) (10, 0) (10, 10) 6 / \ 7 (0, 10) (0, 10) 8These examples illustrate the possible moves and resulting pairs of numbers in Euclid's Game for different starting pairs. The game tree expands as players make their moves, and it shows all possible paths the game can take until one player cannot make a move.part b) Choosing to Move First or Second:In Euclid's Game, it is generally advantageous to move first. This is because the first player has more choices of moves, and they can often force the second player into a losing position. However, the second player can still win if they play strategically.Here are some tips for choosing whether to move first or second in Euclid's Game:If the starting numbers are relatively close together, it is generally better to move first.If the starting numbers are far apart, it may be better to move second. This is because the first player may have to make a suboptimal move early in the game, which could give the second player an advantage.If you are a good strategist, you may be able to win even if you move second. However, if you are not confident in your ability to outplay your opponent, it is generally safer to move first.