| 1. Show that for any integers m, n the equations w + x + 2y + 2z = m, 2w - 2x + y - z = n have a solution in integers. |
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| 2. Show that the product of four consecutive integers cannot be a square. |
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| 3. A circle or radius R rolls around the inside of a circle of radius 2R, what is the path traced out by a point on its circumference? |
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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