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        riddles >> medium >> Billiard in a triangle table
        
(Message started by: cool_joh on Jul 3^rd, 2008, 8:05pm)

Title: Billiard in a triangle table
Post by cool_joh on Jul 3^rd, 2008, 8:05pm

A game of billiards is played on a triangular table with angles 30 deg, 60 deg and 90 deg. There are pockets at each corner. A ball is hit from just outside the 30 deg pocket towards the middle of the opposite side. Show that if it goes far enough it will end up in the 60 deg pocket after hitting the edge 8 times.

Title: Re: Billiard in a triangle table
Post by Barukh on Jul 4^th, 2008, 8:34am

[hide]Mirrors?[/hide]

Title: Re: Billiard in a triangle table
Post by cool_joh on Jul 4^th, 2008, 5:47pm

I've tried that, but it's still quite hard. I haven't solved this, by the way.

Title: Re: Billiard in a triangle table
Post by Grimbal on Jul 5^th, 2008, 2:50am

Just ... unfold it!

Title: Re: Billiard in a triangle table
Post by capricafox on Jul 12^th, 2008, 5:12pm

First, the 30 degres indicate it is half an equilateral triangle.

2nd, every rail is treated as a mirror, and therefore, this triangle assembles into 2x and 4x version of itself.

The 4th rail is the middle of the table longest side, i.e. the middle of the 2x triangle opposite side. The middle of the 4x triangle opposite side is just the 60 degres pocket. See image.