| 1. How many integers (1) have 5 decimal digits, (2) have last digit 6, and (3) are divisible by 3? |
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| 2. A straight line is drawn on an 8 x 8 chessboard. What is the largest possible number of the unit squares with interior points on the line? |
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| 3. An acute-angled triangle has circumradius R. Show that any interior point of the triangle other than the circumcenter is a distance > R from at least one vertex and a distance < R from at least one vertex. |
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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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(C) John Scholes
jscholes@kalva.demon.co.uk
6 January 2003