Today Puzzle #691
Puzzle No. 691 鈥� Friday 6 March
Artificial intelligence programs have defeated the world’s best in Chess and recently Go. It is estimated that Chess has approximately 10 to the power 45 possible positions. Go is said to have approximately 10 to the power 170 possible positions. Let’s consider a game many children play near perfectly, noughts and crosses (tic tac toe). How many possible board positions are there for noughts and crosses games?
Today’s #PuzzleForToday has been set by Dr Daniel Cowley and Dr Tom Todd, data scientists at Adarga.ai
Click here for the answer
Taking no symmetries or rules of the game into account:
Total board configurations 3^9 = 19,683
Total possible games (sequences of moves) 9! = 362,880
Taking board symmetries and rules of the game into account:
Total board configurations: 5478
Total games: 31,896
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