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As soon as you cross the river, you find a Kabuliwala. You ask him for help to reach Kabul as soon as possi- ble. He says that he will show you the way to Kabul if you help him with the answer of a question. First he explains you the game of CROSS- ZERO. “This game is played on a matrix of 3x3. In this game, the players try to get three circles or three crosses in a row (horizontal, vertical, or diagonal). A player always tries to win, i.e., if a player can place his own symbol (X or O) in a row that already contains two of his own symbols, he will do so. A player always tries to avoid that his opponent wins, i.e., if a player can place his own symbol (X or O) in a row that already contains two of the symbols of his opponent, he will do so.” The question he asks is that Khaled and Shahzia play a game of Cross-Zero. Khaled plays with crosses (X) and Shahzia plays with circles (O), however we don’t know who started the game. The players are intelli- gent enough and maintain the rules. After six turns into the game the matrix looks like- So who will win the game ? |
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Answer» Any one can win depending on the initial move It is clear that if we know who made the sixth move, we also know who can make the seventh move andwins. If Shahzia (circles) has made the sixth move, there are three possibilities for the situation after five moves: Based on the rules of the game, only possibility 1 could have resulted in the situation after six moves. Inthat case, there are three possibilities for the situation after four moves: Based on the rules of the game, Khaled (crosses) would have made the winning move, which however did not happen. From this, we can conclude that Khaled did not make the fifth move and Shahzia did not make the sixth move. THEREFORE, Khaled must have made the sixth move and Shahzia can make the seventh, winning move! To CHECK that Khaled could indeed have made the sixth move, we look at the following three possibilities after five moves: Based on the rules of the game, only possibility 3 can result in the situation after six moves. Therefore, Khaled could indeed have made the sixth move. HENCE, Khaled has made the sixth move, and Shahzia will make the seventh move and win. |
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