| 1. Each button in a box is big or small, and white or black. There is at least one big button, at least one small button, at least one white button, and at least one black button. Show that there are two buttons with different size and color. |
|
| 2. m and n are different positive integers. Show that 22m + 1 and 22n + 1 are coprime. |
|
| 3. T is a triangle. Show that there is a triangle T' whose sides are equal to the medians of T, and that T'' is similar to T. |
|
The original problems are in Hungarian. They are available on the KöMaL archive on the web. They are also available in English (with solutions) in: Andy Liu, Hungarian Problem Book III, 1929-1943, MAA 2001. ISBN 0883856441.
Eötvös home
(C) John Scholes
jscholes@kalva.demon.co.uk
6 January 2003
Last corrected/updated 6 Jan 03