| 1. Given any six points in the plane, no three collinear, show that we can always find three which form an obtuse-angled triangle with one angle at least 120o. | |
| 2. Show that if m and n are integers such that m2 + mn + n2 is divisible by 9, then they must both be divisible by 3. | |
| 3. The hexagon ABCDEF is convex and opposite sides are parallel. Show that the triangles ACE and BDF have equal area. |
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