| 1. Let S be the set of points with coordinates (m, n), where 0 <= m, n < p. Show that we can find p points in S with no three collinear. | |
| 2. A triangle ABC has incenter I and circumcenter O. The orthocenter of the three points at which the incircle touches its sides is X. Show that I, O and X are collinear. | |
| 3. Show that the edges of a planar graph can be colored with three colors so that there is no monochromatic circuit. |
The original problems are in Hungarian. Many thanks to Péter Dombi for the translation.
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John Scholes
jscholes@kalva.demon.co.uk
20 May 2002
Last corrected/updated 28 Apr 03