43rd Swedish 2003 Problem 1 The real numbers w, x, y, z are all non-negative and satisfy: y = x - 2003, z = 2y - 2003, w = 3z - 2003. Find the solution with the smallest x.
x = 2003·5/3, y = 2003·2/3, z = 2003/3, w = 0. Solution z = w/3 + 2003/3, y = z/2 + 2003/2 = w/6 + 2003·2/3, x = y + 2003 = w/6 + 2003·5/3. 43rd Swedish 2003 © John Scholes jscholes@kalva.demon.co.uk 11 January 2004 Last corrected/updated 11 Jan 04