| 1. E is the product 2·4·6 ... 2n, and D is the product 1·3·5 ... (2n-1). Show that, for some m, D·2m is a multiple of E. |
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| 2. Given a circle, find the inscribed polygon with the largest sum of the squares of its sides. |
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| 3. For i and j positive integers, let Rij be the rectangle with vertices at (0, 0), (i, 0), (0, j), (i, j). Show that any infinite set of Rij must have two rectangles one of which covers the other. |
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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: Andy Liu, Hungarian Problem Book III, 1929-1943, MAA 2001. ISBN 0883856441.
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© John Scholes
jscholes@kalva.demon.co.uk
6 January 2003
Last corrected/updated 3 Nov 03