benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Find the number of subsets S of {1,2,…,48} satisfying both of the following properties: - For each integer 1≤k≤24, exactly one of 2k−1 and 2k is in S. - There are exactly nine inte…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find the number of subsets SS of {1,2,…,48}\{1,2, \ldots, 48\} satisfying both of the following properties: - For each integer 1≤k≤241 \leq k \leq 24, exactly one of 2k−12 k-1 and 2k2 k is in SS. - There are exactly nine integers 1≤m≤471 \leq m \leq 47 so that both mm and m+1m+1 are in SS.
Plain-text mathematical notation (without MathML)
Find the number of subsets S of {1,2,…,48} satisfying both of the following properties: - For each integer 1≤k≤24, exactly one of 2k−1 and 2k is in S. - There are exactly nine integers 1≤m≤47 so that both m and m+1 are in S.
Original LaTeX notation
Find the number of subsets $S$ of $\{1,2, \ldots, 48\}$ satisfying both of the following properties: - For each integer $1 \leq k \leq 24$, exactly one of $2 k-1$ and $2 k$ is in $S$. - There are exactly nine integers $1 \leq m \leq 47$ so that both $m$ and $m+1$ are in $S$.

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
62a6afbd-3ca1-5a59-8cbf-e432c26a53dd
task_key
test--62a6afbd-3ca1-5a59-8cbf-e432c26a53dd
task_revision_id
1
config / split
/ test

Official source

initial import