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Omni-MATH / Will stands at a point P on the edge of a circular room with perfectly reflective walls. He shines two laser pointers into the room, forming angles of n^(∘) and (n+1)^(∘) with the …

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problem

Will stands at a point PP on the edge of a circular room with perfectly reflective walls. He shines two laser pointers into the room, forming angles of n∘n^{\circ} and (n+1)∘(n+1)^{\circ} with the tangent at PP, where nn is a positive integer less than 90. The lasers reflect off of the walls, illuminating the points they hit on the walls, until they reach PP again. (PP is also illuminated at the end.) What is the minimum possible number of illuminated points on the walls of the room?
Plain-text mathematical notation (without MathML)
Will stands at a point P on the edge of a circular room with perfectly reflective walls. He shines two laser pointers into the room, forming angles of n^(∘) and (n+1)^(∘) with the tangent at P, where n is a positive integer less than 90. The lasers reflect off of the walls, illuminating the points they hit on the walls, until they reach P again. (P is also illuminated at the end.) What is the minimum possible number of illuminated points on the walls of the room?
Original LaTeX notation
Will stands at a point \(P\) on the edge of a circular room with perfectly reflective walls. He shines two laser pointers into the room, forming angles of \(n^{\circ}\) and \((n+1)^{\circ}\) with the tangent at \(P\), where \(n\) is a positive integer less than 90. The lasers reflect off of the walls, illuminating the points they hit on the walls, until they reach \(P\) again. (\(P\) is also illuminated at the end.) What is the minimum possible number of illuminated points on the walls of the room?

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Source and history

task_id
8c5fee4a-a171-5109-a22e-0309024ab73a
task_key
test--8c5fee4a-a171-5109-a22e-0309024ab73a
task_revision_id
1
config / split
/ test

Official source

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