 Hello everyone, this is Alice Gao. In this video, I will go through the process of solving the question in lecture 3 on slide 30. In this problem, we relax the eight puzzle by removing both constraints. When we move a tile from square A to square B, A and B do not need to be adjacent, and B doesn't have to be empty. What admissible heuristic function can we derive using this relaxed problem? The correct answer is B, the misplaced tile heuristic. Consider one state of the eight puzzle. We need to determine the smallest number of moves to transform this state to a goal state. In other words, how many moves does it take to move all the tiles into their goal positions? We have removed both constraints, which means that we can move a tile from one square to any other square instantly. In other words, a tile can fly from one square to another square. This is great. This means that if a tile is not in its goal position, we can move it to its goal position in one step. For this state, we need seven moves, since all eight tiles, except tile six, are not in their goal positions. What are we really computing here? The number of moves is equal to the number of tiles that are not in their goal positions. This number is equal to the value of the misplaced tile heuristic. The correct answer is B, the misplaced tile heuristic. Thank you very much for watching. I will see you in the next video. Bye for now.