| 1. The positive integers a, b, c are such that there are triangles with sides an, bn, cn for all positive integers n. Show that at least two of a, b, c must be equal. |
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| 2. What is the locus of the point (in the plane), the sum of whose distances to a given point and line is fixed? |
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| 3. Given three points in the plane, how does one construct three distinct circles which touch in pairs at the three points? |
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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