| 1. Coins denomination 1, 2, 10, 20 and 50 are available. How many ways are there of paying 100? |
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| 2. Show that ∑i=0 to k nCi (-x)i is positive for all 0 ≤ x < 1/n and all k ≤ n, where nCi is the binomial coefficient. |
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| 3. L, M, N are three lines through a point such that the angle between any pair is 60o. Show that the set of points P in the plane of ABC whose distances from the lines L, M, N are less than a, b, c respectively is the interior of hexagon iff there is a triangle with sides a, b, c. Find the perimeter of this hexagon. |
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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 2 Nov 03