benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / The integer numbers from 1 to 2002 are written in a blackboard in increasing order 1,2,…,2001,2002. After that, somebody erases the numbers in the (3k+1)−th places i.e. (1,4,7,…). …

Problem

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

problem

The integer numbers from 11 to 20022002 are written in a blackboard in increasing order 1,2,…,2001,20021,2,\ldots, 2001,2002. After that, somebody erases the numbers in the (3k+1)−th (3k+1)-th places i.e. (1,4,7,…)(1,4,7,\dots). After that, the same person erases the numbers in the (3k+1)−th(3k+1)-th positions of the new list (in this case, 2,5,9,…2,5,9,\ldots). This process is repeated until one number remains. What is this number?
Plain-text mathematical notation (without MathML)
The integer numbers from 1 to 2002 are written in a blackboard in increasing order 1,2,…,2001,2002. After that, somebody erases the numbers in the (3k+1)−th places i.e. (1,4,7,…). After that, the same person erases the numbers in the (3k+1)−th positions of the new list (in this case, 2,5,9,…). This process is repeated until one number remains. What is this number?
Original LaTeX notation
The integer numbers from $1$ to $2002$ are written in a blackboard in increasing order $1,2,\ldots, 2001,2002$. After that, somebody erases the numbers in the $ (3k+1)-th$ places i.e. $(1,4,7,\dots)$. After that, the same person erases the numbers in the $(3k+1)-th$ positions of the new list (in this case, $2,5,9,\ldots$). This process is repeated until one number remains. What is this number?

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
3f9bb3fa-986c-515f-b509-dd08121ae479
task_key
test--3f9bb3fa-986c-515f-b509-dd08121ae479
task_revision_id
1
config / split
/ test

Official source

initial import