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Omni-MATH / Meghal is playing a game with 2016 rounds 1,2,⋯,2016. In round n, two rectangular double-sided mirrors are arranged such that they share a common edge and the angle between the fac…

Problem

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problem

Meghal is playing a game with 2016 rounds 1,2,⋯,20161,2, \cdots, 2016. In round nn, two rectangular double-sided mirrors are arranged such that they share a common edge and the angle between the faces is 2πn+2\frac{2 \pi}{n+2}. Meghal shoots a laser at these mirrors and her score for the round is the number of points on the two mirrors at which the laser beam touches a mirror. What is the maximum possible score Meghal could have after she finishes the game?
Plain-text mathematical notation (without MathML)
Meghal is playing a game with 2016 rounds 1,2,⋯,2016. In round n, two rectangular double-sided mirrors are arranged such that they share a common edge and the angle between the faces is (2π)/(n+2). Meghal shoots a laser at these mirrors and her score for the round is the number of points on the two mirrors at which the laser beam touches a mirror. What is the maximum possible score Meghal could have after she finishes the game?
Original LaTeX notation
Meghal is playing a game with 2016 rounds $1,2, \cdots, 2016$. In round $n$, two rectangular double-sided mirrors are arranged such that they share a common edge and the angle between the faces is $\frac{2 \pi}{n+2}$. Meghal shoots a laser at these mirrors and her score for the round is the number of points on the two mirrors at which the laser beam touches a mirror. What is the maximum possible score Meghal could have after she finishes the game?

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Source and history

task_id
f69daca4-a14b-5312-8c8e-06b571bc52db
task_key
test--f69daca4-a14b-5312-8c8e-06b571bc52db
task_revision_id
1
config / split
/ test

Official source

initial import