| 1. n cards are dealt to two players. Each player has at least one card. How many possible hands can the first player have? |
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| 2. ABC is a right-angled triangle. Construct a point P inside ABC so that the angles PAB, PBC, PCA are equal. |
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| 3. A triangle ABC has sides BC = a, CA = b, AB = c. Given (1) the radius R of the circumcircle, (2) a, (3) t = b/c, determine b, c and the angles A, B, C. |
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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 1, 1894-1905, 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 6 Jan 03