Question

Consider the Nim game: There are n number of tokens. Each player is required to divide the pile of tokens into two piles of unequal tokens. The player who cannot divide any pile further looses the game. Solve it with n = 5 using minimax algorithm. Assume MAX takes first move. Also show the path for MAX's win. =

Answer 1

To win the Nim game with n = 5 using the minimax algorithm, MAX should first divide the pile into 2 and 3, ensuring the opponent cannot make a further unequal division.

Step-by-step explanation:

The question pertains to solving the Nim game with n = 5 using the minimax algorithm. In this situation, MAX, the first player, aims to force the opponent into a position where they cannot divide the piles further. Starting with 5 tokens, MAX has two options: divide into piles of 1 and 4, or 2 and 3.

If MAX splits them into 1 and 4, the next player can still split the pile of 4 into 1 and 3, leaving MAX with a divisible pile again, which is not ideal for MAX. However, if MAX divides 5 into piles of 2 and 3, the next player has no option but to divide 2 into 1 and 1 or 3 into 1 and 2. Both lead to piles that cannot be divided unequally anymore, causing the next player to lose and thus enabling MAX to win.