| 1. Prove that sin x + ½ sin 2x + (1/3) sin 3x > 0 for 0 < x < 180o. |
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| 2. P is a point on the base of an isosceles triangle. Lines parallel to the sides through P meet the sides at Q and R. Show that the reflection of P in the line QR lies on the circumcircle of the triangle. |
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| 3. Which positive integers cannot be represented as a sum of (two or more) consecutive integers? |
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The original problems are in Hungarian. They are available on the KöMaL archive on the web.
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(C) John Scholes
jscholes@kalva.demon.co.uk
24 Mar 2003
Last corrected/updated 24 Mar 2003