benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / A number of N children are at a party and they sit in a circle to play a game of Pass and Parcel. Because the host has no other form of entertainment, the parcel has infinitely man…

Problem

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

problem

A number of NN children are at a party and they sit in a circle to play a game of Pass and Parcel. Because the host has no other form of entertainment, the parcel has infinitely many layers. On turn ii, starting with i=1i=1, the following two things happen in order: [b](1)(1)[/b] The parcel is passed i2i^2 positions clockwise; and [b](2)(2)[/b] The child currently holding the parcel unwraps a layer and claims the prize inside. For what values of NN will every chidren receive a prize? PatrickWinterUnitedKingdomPatrick \ Winter \, United \ Kingdom
Plain-text mathematical notation (without MathML)
A number of N children are at a party and they sit in a circle to play a game of Pass and Parcel. Because the host has no other form of entertainment, the parcel has infinitely many layers. On turn i, starting with i=1, the following two things happen in order:
[b](1)[/b] The parcel is passed i² positions clockwise; and
[b](2)[/b] The child currently holding the parcel unwraps a layer and claims the prize inside.
For what values of N will every chidren receive a prize?
                                                                                                                                           
   Patrick Winter United Kingdom
Original LaTeX notation
A number of $N$ children are at a party and they sit in a circle to play a game of Pass and Parcel. Because the host has no other form of entertainment, the parcel has infinitely many layers. On turn $i$, starting with $i=1$, the following two things happen in order:
[b]$(1)$[/b] The parcel is passed $i^2$ positions clockwise; and
[b]$(2)$[/b] The child currently holding the parcel unwraps a layer and claims the prize inside.
For what values of $N$ will every chidren receive a prize?
                                                                                                                                           
   $Patrick \ Winter \, United \ Kingdom$

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
c1cd20e0-cad2-59b9-9bd2-379ea61c13ef
task_key
test--c1cd20e0-cad2-59b9-9bd2-379ea61c13ef
task_revision_id
1
config / split
/ test

Official source

initial import