In a standard 3x3 tictatoe there are 8 distinct possibilities to create “three in a row”
3 horizontal, 3 vertical and 2 diagonal.
How many ways are there in a threedimensional 5x5x5 tictactoe?
How about 6x6x6 ?
Assuming my solutions are correct here's how to generalize to nxnxn with n≥4
7's are at the 2x2x2 corner cubes at each of the 8 corners (I'll divide by 2 at this step.)
7x8x8/2 = 224
11's are on the edges. 2x2x(n4) for each of the 12 edges
2x2x(n4)x12/2 = 264(n4)
17's are at the face centers. 2x(n4)² for each of the 6 faces
2x(n4)²x6/2 = 102(n4)²
26's are at the very center. 26x(n4)³/2 = 13(n4)³
For a grand total of
224 + 264(n4) +102(n4)² + 13(n4)³
This formula checks for n=5 and n=6, assuming those answers were correct.

Posted by Jer
on 20141023 10:18:48 