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Omni-MATH / Three players play tic-tac-toe together. In other words, the three players take…

Problem

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problem

Three players play tic-tac-toe together. In other words, the three players take turns placing an "A", "B", and "C", respectively, in one of the free spots of a 3×33 \times 3 grid, and the first player to have three of their label in a row, column, or diagonal wins. How many possible final boards are there where the player who goes third wins the game? (Rotations and reflections are considered different boards, but the order of placement does not matter.)
Plain-text mathematical notation (without MathML)
Three players play tic-tac-toe together. In other words, the three players take turns placing an "A", "B", and "C", respectively, in one of the free spots of a 3×3 grid, and the first player to have three of their label in a row, column, or diagonal wins. How many possible final boards are there where the player who goes third wins the game? (Rotations and reflections are considered different boards, but the order of placement does not matter.)
Original LaTeX notation
Three players play tic-tac-toe together. In other words, the three players take turns placing an "A", "B", and "C", respectively, in one of the free spots of a $3 \times 3$ grid, and the first player to have three of their label in a row, column, or diagonal wins. How many possible final boards are there where the player who goes third wins the game? (Rotations and reflections are considered different boards, but the order of placement does not matter.)

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Source and history

task_id
6c22e427-91ac-58e5-ba53-5314b8ede1fa
task_key
test--6c22e427-91ac-58e5-ba53-5314b8ede1fa
task_revision_id
1
config / split
/ test

Official source

initial import