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3D Tic Tac Toe from "Building Thinking Classrooms"

This resource was made to accompany the 3D Tic Tac Toe Exercise from Building Thinking Classrooms by Peter Liljedahl.

THE PROBLEM:

THE PROBLEM:
In a standard game of tic-tac-toe, a win occurs when 3 X’s or 3 O’s are all in a row (collinear). There are 8 ways for a win in a standard game of tic-tac-toe: 3 up and down, 3 side to side, and 2 diagonally. How many ways are there to win in 3D tic-tac-toe, where the rules are the same: a win is 3 collinear X’s or O’s?

This construction was made to help you visualize this problem. Drag a LARGE BLACK POINT to move a cube. Click on the point to move it up or down. Click on it again to move it to the side.

Slide the slider n above so n = 4. How many ways are there to win in a 3D-Tic-Tac-Toe game where the object of the game is to get 4 collinear X's or O's?

Slide the slider n above so n = 5. How many ways are there to win in a 3D-Tic-Tac-Toe game where the object of the game is to get 5 collinear X's or O's?