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1. ABCD is a square. E is a point on the side BC such that BE = BC/3, and F is a point on the ray DC such that CF = DC/2. Prove that the lines AE and BF intersect on the circumcircle of the square.
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| 2. For which m > 1 is (m-1)! divisible by m? |
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| 3. An open half-plane is the set of all points lying to one side of a line, but excluding the points on the line itself. If four open half-planes cover the plane, show that one can select three of them which still cover the plane. |
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The original problems are in Hungarian. Many thanks to Péter Dombi for the translation.
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(C) John Scholes
jscholes@kalva.demon.co.uk
19 Apr 2003
Last corrected/updated 19 Apr 2003