Ask Question
25 April, 06:10

Suppose a game of 3-D tic tac toe is played on a 6x6x6 cube. How many winning lines of 6-in-a-row are there through the cube?

+5
Answers (1)
  1. 25 April, 06:32
    0
    On a cube of side k and n dimensions, there are

    [ (k+2) ⁿ - kⁿ] / 2

    winning lines.

    In your case,

    k = 6

    n = 3

    Therefore:

    [ (6+2) ³ - 6³] / 2

    = (8 ³ - 6³) / 2

    = (512 - 216) / 2

    = 148

    Hence, there are 148 6-in-a-row winning lines through the cube.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “Suppose a game of 3-D tic tac toe is played on a 6x6x6 cube. How many winning lines of 6-in-a-row are there through the cube? ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers