| 1. For what positive integers n, k (with k < n) are the binomial coefficients nC(k-1), nCk and nC(k+1) three successive terms of an arithmetic progression? | |
| 2. For any positive real r, let d(r) be the distance of the nearest lattice point from the circle center the origin and radius r. Show that d(r) tends to zero as r tends to infinity. | |
| 3. n > 4 planes are in general position (so every 3 planes have just one common point, and no point belongs to more than 3 planes). Show that there are at least (2n-3)/4 tetrahedra among the regions formed by the planes. |
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