benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / There are N lockers, labeled from 1 to N, placed in clockwise order around a circular hallway. Initially, all lockers are open. Ansoon starts at the first locker and always moves c…

Problem

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

problem

There are NN lockers, labeled from 1 to NN, placed in clockwise order around a circular hallway. Initially, all lockers are open. Ansoon starts at the first locker and always moves clockwise. When she is at locker nn and there are more than nn open lockers, she keeps locker nn open and closes the next nn open lockers, then repeats the process with the next open locker. If she is at locker nn and there are at most nn lockers still open, she keeps locker nn open and closes all other lockers. She continues this process until only one locker is left open. What is the smallest integer N>2021N>2021 such that the last open locker is locker 1?
Plain-text mathematical notation (without MathML)
There are N lockers, labeled from 1 to N, placed in clockwise order around a circular hallway. Initially, all lockers are open. Ansoon starts at the first locker and always moves clockwise. When she is at locker n and there are more than n open lockers, she keeps locker n open and closes the next n open lockers, then repeats the process with the next open locker. If she is at locker n and there are at most n lockers still open, she keeps locker n open and closes all other lockers. She continues this process until only one locker is left open. What is the smallest integer N>2021 such that the last open locker is locker 1?
Original LaTeX notation
There are $N$ lockers, labeled from 1 to $N$, placed in clockwise order around a circular hallway. Initially, all lockers are open. Ansoon starts at the first locker and always moves clockwise. When she is at locker $n$ and there are more than $n$ open lockers, she keeps locker $n$ open and closes the next $n$ open lockers, then repeats the process with the next open locker. If she is at locker $n$ and there are at most $n$ lockers still open, she keeps locker $n$ open and closes all other lockers. She continues this process until only one locker is left open. What is the smallest integer $N>2021$ such that the last open locker is locker 1?

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
f89fa728-5385-5816-9075-ebcf7cf984da
task_key
test--f89fa728-5385-5816-9075-ebcf7cf984da
task_revision_id
1
config / split
/ test

Official source

initial import