benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A dance with 2018 couples takes place in Havana. For the dance, 2018 distinct…

Problem

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

problem

A dance with 2018 couples takes place in Havana. For the dance, 2018 distinct points labeled 0,1,…,20170, 1,\ldots, 2017 are marked in a circumference and each couple is placed on a different point. For i≥1i\geq1, let $s_i=i\ (\textrm{mod}\ 2018)$ and $r_i=2i\ (\textrm{mod}\ 2018)$. The dance begins at minute 00. On the ii-th minute, the couple at point sis_i (if there's any) moves to point rir_i, the couple on point rir_i (if there's any) drops out, and the dance continues with the remaining couples. The dance ends after 201822018^2 minutes. Determine how many couples remain at the end. Note: If ri=sir_i=s_i, the couple on sis_i stays there and does not drop out.
Plain-text mathematical notation (without MathML)
A dance with 2018 couples takes place in Havana. For the dance, 2018 distinct points labeled 0,1,…,2017 are marked in a circumference and each couple is placed on a different point. For i≥1, let $s_i=i\ (\textrm{mod}\ 2018)$ and $r_i=2i\ (\textrm{mod}\ 2018)$. The dance begins at minute 0. On the i-th minute, the couple at point s_(i) (if there's any) moves to point r_(i), the couple on point r_(i) (if there's any) drops out, and the dance continues with the remaining couples. The dance ends after 2018² minutes. Determine how many couples remain at the end. 

Note: If r_(i)=s_(i), the couple on s_(i) stays there and does not drop out.
Original LaTeX notation
A dance with 2018 couples takes place in Havana. For the dance, 2018 distinct points labeled $0, 1,\ldots, 2017$ are marked in a circumference and each couple is placed on a different point. For $i\geq1$, let $s_i=i\ (\textrm{mod}\ 2018)$ and $r_i=2i\ (\textrm{mod}\ 2018)$. The dance begins at minute $0$. On the $i$-th minute, the couple at point $s_i$ (if there's any) moves to point $r_i$, the couple on point $r_i$ (if there's any) drops out, and the dance continues with the remaining couples. The dance ends after $2018^2$ minutes. Determine how many couples remain at the end. 

Note: If $r_i=s_i$, the couple on $s_i$ stays there and does not drop out.

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
c6934d81-a5c2-51dc-a9be-6544df280429
task_key
test--c6934d81-a5c2-51dc-a9be-6544df280429
task_revision_id
1
config / split
/ test

Official source

initial import