Artificial Intelligence - Adversarial Search 1. Consider the following three variants of minimax search: the simple version, alpha-beta search, and depth-limited search, and consider the games of tic-tac-toe and chess. For the chess game, suppose that the Threefold Repetition Rule and the Fifty-Move Rule, and the similar rules if any, are not considered, i.e., the game will not terminate if the same position occurs multiple times. For each combination of minimax variant and game, answer the following question: can that minimax variant possibly never terminate, in computing the best next move? Justify your answer.

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Eight puzzle problem

The N-puzzle problem contains N tiles (N+1 including empty tiles) where the value of N can be 8, 15, 24, etc. The puzzle is divided into the square root of (N+1) rows and the square root of (N+1) columns. These problems have an initial state or configuration and a goal state or configuration. The puzzle can be solved by shifting the tiles one by one in the empty space. The objective is to place the numbers on the tiles to match the final state using the empty space. The other name for the N-puzzle problem is the sliding puzzle.