| 1. Every point in space is colored with one of 5 colors. Prove that there are four coplanar points with different colors. | |
| 2. n > 1 is an odd integer. Show that there are positive integers a and b such that 4/n = 1/a + 1/b iff n has a prime divisor of the form 4k-1. | |
| 3. There are two groups of tennis players, one of 1000 players and the other of 1001 players. The players can ranked according to their ability. A higher ranking player always beats a lower ranking player (and the ranking never changes). We know the ranking within each group. Show how it is possible in 11 games to find the player who is 1001st out of 2001. |
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