{"status": "success", "data": {"description_md": "Ansh has a $10$-dimensional hypercube, where every point in the hypercube is a point $(x_1,x_2,\\ldots,x_{10})$ with $x_i \\in \\{0,1,2\\}$ for $1 \\le i \\le 10$. He wants to play tic-tac-toe, but he doesn't have any friends. He wants to count the number of ways to get $3$ in a row (where space diagonals are allowed), which occurs when the three selected points are collinear in $10$-dimensional Euclidean space. The number of ways for Ansh to get $3$ in a row can be written as $2^a\\cdot b$, where $a$ and $b$ are positive integers and $b$ is odd. Find the value of $a$.", "description_html": "

Ansh has a 10-dimensional hypercube, where every point in the hypercube is a point (x_1,x_2,\\ldots,x_{10}) with x_i \\in \\{0,1,2\\} for 1 \\le i \\le 10. He wants to play tic-tac-toe, but he doesn’t have any friends. He wants to count the number of ways to get 3 in a row (where space diagonals are allowed), which occurs when the three selected points are collinear in 10-dimensional Euclidean space. The number of ways for Ansh to get 3 in a row can be written as 2^a\\cdot b, where a and b are positive integers and b is odd. Find the value of a.

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