I jumped straight to 'X wins, O wins, draw' and thought I was done.
Start by clarifying the definition of an end game state (win, loss, draw) and the rules (3x3 board, X goes first). Then systematically enumerate all possible terminal board configurations, using symmetry to reduce redundancy and ensure completeness. Conclude by discussing the implications for algorithm design, such as minimax or game tree pruning.
Pro tip: Mention that there are exactly 958 terminal board states (including symmetries) and that using symmetry reduces the analysis to 138 unique states. This shows depth and efficiency, and ties into Apple's emphasis on optimization.
Confirm the standard 3x3 tic-tac-toe rules: X moves first, players alternate, and a game ends when a player gets three in a row or the board is full (draw). Define what constitutes an end game state.
List all possible winning lines: 3 rows, 3 columns, 2 diagonals. For each, consider which player (X or O) can win and the possible board configurations that lead to that win, ensuring no earlier win occurred.
Identify board states where all 9 cells are filled and no player has three in a row. Note that draws are only possible if neither player wins on the final move.
Use rotations and reflections to group equivalent board states. Explain that there are 8 symmetries (including identity) and that many terminal states are equivalent under these transformations.
State the total number of terminal states (958) and unique states after symmetry (138). Discuss how this enumeration informs game tree search, minimax, and pruning strategies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.