| 1. A and B are any two subsets of {1, 2, ... , n-1} such that |A| + |B| > n-1. Prove that one can find a in A and b in B such that a + b = n. |
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| 2. n and d are positive integers such that d divides 2n2. Prove that n2 + d cannot be a square. |
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| 3. ABCDEF is a convex hexagon with all its sides equal. Also A + C + E = B + D + F. Show that A = D, B = E and C = F. |
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The original problems are in Hungarian. Many thanks to Péter Dombi for the translation.
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(C) John Scholes
jscholes@kalva.demon.co.uk
19 Apr 2003
Last corrected/updated 19 Apr 2003