| 1. Show that the number of ordered pairs (a, b) of positive integers with lowest common multiple n is the same as the number of positive divisors of n2. | |
| 2. Show that given any n+1 diagonals of a convex n-gon, one can always find two which have no common point. | |
| 3. P is any point of the tetrahedron ABCD except D. Show that at least one of the three distances DA, DB, DC exceeds at least one of the distances PA, PB and PC. |
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