benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / Let ABC be an equilateral triangle. From the vertex A we draw a ray towards the interior of the triangle such that the ray reaches one of the sides of the triangle. When the ray re…

Problem

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

problem

Let ABCABC be an equilateral triangle. From the vertex AA we draw a ray towards the interior of the triangle such that the ray reaches one of the sides of the triangle. When the ray reaches a side, it then bounces off following the law of reflection, that is, if it arrives with a directed angle α\alpha, it leaves with a directed angle 180∘−α180^{\circ}-\alpha. After nn bounces, the ray returns to AA without ever landing on any of the other two vertices. Find all possible values of nn.
Plain-text mathematical notation (without MathML)
Let ABC be an equilateral triangle. From the vertex A we draw a ray towards the interior of the triangle such that the ray reaches one of the sides of the triangle. When the ray reaches a side, it then bounces off following the law of reflection, that is, if it arrives with a directed angle α, it leaves with a directed angle 180^(∘)−α. After n bounces, the ray returns to A without ever landing on any of the other two vertices. Find all possible values of n.
Original LaTeX notation
Let $ABC$ be an equilateral triangle. From the vertex $A$ we draw a ray towards the interior of the triangle such that the ray reaches one of the sides of the triangle. When the ray reaches a side, it then bounces off following the law of reflection, that is, if it arrives with a directed angle $\alpha$, it leaves with a directed angle $180^{\circ}-\alpha$. After $n$ bounces, the ray returns to $A$ without ever landing on any of the other two vertices. Find all possible values of $n$.

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
fc599dd5-b177-55fa-a1bb-e22519d06260
task_key
test--fc599dd5-b177-55fa-a1bb-e22519d06260
task_revision_id
1
config / split
/ test

Official source

initial import