benchmarks.wiki / Public workspace
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Omni-MATH / Let C be a cube of side length 2. We color each of the faces of C blue, then subdivide it into 2³=8 unit cubes. We then randomly rearrange these cubes (possibly with rotation) to f…
Problem
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problem
Let be a cube of side length 2. We color each of the faces of blue, then subdivide it into unit cubes. We then randomly rearrange these cubes (possibly with rotation) to form a new 3-dimensional cube. What is the probability that its exterior is still completely blue?
Plain-text mathematical notation (without MathML)
Let C be a cube of side length 2. We color each of the faces of C blue, then subdivide it into 2³=8 unit cubes. We then randomly rearrange these cubes (possibly with rotation) to form a new 3-dimensional cube. What is the probability that its exterior is still completely blue?
Original LaTeX notation
Let $\mathcal{C}$ be a cube of side length 2. We color each of the faces of $\mathcal{C}$ blue, then subdivide it into $2^{3}=8$ unit cubes. We then randomly rearrange these cubes (possibly with rotation) to form a new 3-dimensional cube. What is the probability that its exterior is still completely blue?Discussion
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Source and history
- task_id
bcef91f8-cfa7-5215-8897-26d748ef339d- task_key
test--bcef91f8-cfa7-5215-8897-26d748ef339d- task_revision_id
- 1
- config / split
- / test
initial import