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Omni-MATH / A nonempty set S is called well-filled if for every m∈S, there are fewer than (1)/(2)m elements of S which are less than m. Determine the number of well-filled subsets of …

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problem

A nonempty set SS is called well-filled if for every m∈Sm \in S, there are fewer than 12m\frac{1}{2}m elements of SS which are less than mm. Determine the number of well-filled subsets of {1,2,…,42}\{1,2, \ldots, 42\}.
Plain-text mathematical notation (without MathML)
A nonempty set S is called well-filled if for every m∈S, there are fewer than (1)/(2)m elements of S which are less than m. Determine the number of well-filled subsets of {1,2,…,42}.
Original LaTeX notation
A nonempty set $S$ is called well-filled if for every $m \in S$, there are fewer than $\frac{1}{2}m$ elements of $S$ which are less than $m$. Determine the number of well-filled subsets of $\{1,2, \ldots, 42\}$.

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task_id
ac8527ac-9e86-54c6-b7a0-99bbec8fd1a2
task_key
test--ac8527ac-9e86-54c6-b7a0-99bbec8fd1a2
task_revision_id
1
config / split
/ test

Official source

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