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Omni-MATH / For each positive integer n let S_(n) denote the set {1,2,3,…,n}. Compute the number of triples of subsets A,B,C of S₂₀₀₆ (not necessarily nonempty or proper) such that A is a subs…

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problem

For each positive integer nn let SnS_{n} denote the set {1,2,3,…,n}\{1,2,3, \ldots, n\}. Compute the number of triples of subsets A,B,CA, B, C of S2006S_{2006} (not necessarily nonempty or proper) such that AA is a subset of BB and S2006−AS_{2006}-A is a subset of CC.
Plain-text mathematical notation (without MathML)
For each positive integer n let S_(n) denote the set {1,2,3,…,n}. Compute the number of triples of subsets A,B,C of S₂₀₀₆ (not necessarily nonempty or proper) such that A is a subset of B and S₂₀₀₆−A is a subset of C.
Original LaTeX notation
For each positive integer $n$ let $S_{n}$ denote the set $\{1,2,3, \ldots, n\}$. Compute the number of triples of subsets $A, B, C$ of $S_{2006}$ (not necessarily nonempty or proper) such that $A$ is a subset of $B$ and $S_{2006}-A$ is a subset of $C$.

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Source and history

task_id
e937335f-f3b5-5b6f-be11-555f50515ef5
task_key
test--e937335f-f3b5-5b6f-be11-555f50515ef5
task_revision_id
1
config / split
/ test

Official source

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