| 1. Given four integers, show that the product of the six differences is divisible by 12. |
|
| 2. How many zeros does the the decimal representation of 1000! end with? |
|
| 3. Show that the inradius of a right-angled triangle is less than 1/4 of the length of the hypoteneuse and less than 1/2 the length of the shortest side. |
|
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): (Translated by Elvira Rapaport) József Kürschák, G Hajós, G Neukomm & J Surányi, Hungarian Problem Book 2, 1906-1928, MAA 1963. Out of print, but available in some university libraries. p>
Eötvös home
John Scholes
jscholes@kalva.demon.co.uk
20 Oct 1999