42nd Swedish 2002

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1.  268 numbers are written around a circle. The 17th number is 3, the 83rd is 4 and the 144th is 9, The sum of every 20 consecutive numbers is 72. Find the 210th number.
2.  A, B, C can walk at 5km/hr. They have a car that can accomodate any two of them whch travels at 50km/hr. Can they reach a point 62km away in less than 3 hrs?
3.  C is the circle center (0,1), radius 1. P is the parabola y = ax2. They meet at (0, 0). For what values of a do they meet at another point or points?
4.  For which integers n ≥8 is n1/(n-7) an integer?
5.  The reals a, b satisfy a3 - 3a2 + 5a - 17 = 0, b3 - 3b2 + 5b + 11 = 0. Find a+b.
6.  A tetrahedron has five edges length 3 and circumradius 2. What is the length of the sixth edge?

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
8 Oct 2003
Last corrected/updated 8 Oct 03