| 1. Given any reals A, B, C, show that An2 + Bn + C < n! for all sufficiently large integers n. |
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| 2. A triangle lies entirely inside a polygon. Show that its perimeter does not exceed the perimeter of the polygon. |
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| 3. Show that a triangle inscribed in a parallelogram has area at most half that of the parallelogram. |
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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.
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John Scholes
jscholes@kalva.demon.co.uk
20 Oct 1999
Last corrected/updated 8 Oct 03