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When a carrom board striker is strike to one side of the board(4 sided), it continue hitting all the side. Does the pattern repeat, assuming the striker doesn't slow and stop.

carrom board striker

I mean, can the point be determined where the striker would strike, after $n$ hits on its side?

José Carlos Santos
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Rajesh Marndi
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  • A lot depends on how it was hit, such as the initial position and initial direction. – For the love of maths Oct 25 '18 at 09:03
  • Yes, with initial position and initial direction, is it possible the path pattern followed by the striker may not repeat??? – Rajesh Marndi Oct 25 '18 at 12:32
  • Assuming perfect reflections from the edges (which are effectively inset from the actual edges), “straighten” the path by tiling the plane with reflections of the board. The criterion for looping is quite simple to state then. – amd Oct 25 '18 at 20:08
  • See this answer for an illustration of the technique. – amd Oct 25 '18 at 20:24

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