| A1. Given a point P inside an acute angle XAY, show how to construct a line through P meeting the line AX at B and the line AY at C such that the area of the triangle ABC is AP2. |
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| A2. Show that x4 - 1993 x3 + (1993 + n) x2 - 11x + n = 0 has at most one integer root if n is an integer. |
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| A3. What is the maximum value f(n) of |s1 - s2| + |s2 - s3| + ... + |sn-1 - sn| over all permutations s1, s2, ... , sn of 1, 2, ... , n? |
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| A4. Find the smallest n > 4 for which we can find a graph on n points with no triangles and such that for every two unjoined points we can find just two points joined to both of them. |
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To avoid possible copyright problems, I have changed the wording, but not the substance, of the problems.
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© John Scholes
jscholes@kalva.demon.co.uk
5 April 2002
Last corrected/updated 18 Dec 2002