Unformatted text preview: (b) Give a brief discussion that will convince us that your answer to part (a) is correct. 4. (a) What are the symmetries of the tic tac toe board game? Ie, what are the ways you can rotate, reﬂect, and/or ﬂip the tic tac toe board, such that the next best move to a board(after it was rotated, reﬂected, etc) is still the next best move after the board was rotated/reﬂected/ﬂipped? (b) Construct the group multiplication table for the symmetries. 5. Consider tic tac toe boards that are completely ﬁlled in with 0’s and × ’s. Use Bernside’s theorem to determine the number of equivalence classes. Note: You may use that a ﬁlled tic tac toe has 5-X’s and 4-O’s or not restrict the number of X’s and O’s. Be sure to specify which assumption you use. 1...
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- Prime number, Cuboctahedron