In the game of Tic Tac Toe, there are 8 distinct winning lines.
Investigate how many distinct winning lines there are in a game played on a 3 by 3 by 3 board, with 27 cells.
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In a game played on a 3 by 3 by 3 board, there are 27 cells. Each of these cells can be marked by a player, creating a total of 3^27 possible ways the game can be played. However, not all of these possible ways are winning lines.
To determine the number of distinct winning lines, we need to consider the different ways that a player can win the game. In Tic Tac Toe, a player wins if they are able to place their markers in all cells of a straight line, either Order a Customized and Comprehensive answer Now
On a 3 by 3 by 3 board, a player can win horizontally, vertically, or diagonally in 3 dimensions. This means that a player can win by placing their markers in all cells of a straight line along the x-axis, the y-axis, or the z-axis. Additionally, a player can also win by placing their markers in all cells of a diagonal line that runs through the board.
In total, this means that there are 3 + 3 + 3 + 1 = 10 distinct winning lines on a 3 by 3 by 3 Tic Tac Toe board. Note that this only counts the distinct lines, and not the number of possible ways that a player can win using each line. For example, the horizontal x-axis winning line can be used to win the game in any of the 3 planes (x = 1, x = 2, x = 3), but Order a Customized and Comprehensive answer Now
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