33rd Swedish 1993 Problem 2 A railway line passes through (in order) the 11 stations A, B, ... , K. The distance from A to K is 56. The distances AC, BD, CE, ... , IK are each ≤ 12. The distances AD, BE, CF, ... , HK are each ≥ 17. Find the distance between B and G.
29 Solution BE + EH + HK ≥ 51 and AK = 56, so AB ≤ 5, so AD = AB + BD ≤ 5 + 12 = 17. But AD ≥ 17. Hence AB = 5, BD = 12, BE = 17. Hence DE = 5. By symmetry, we also have GH = 5, HJ = 12, JK = 5. Hence GK = 5+12+5 = 22. Hence BG = AK - AB - GK = 56 - 5 - 22 = 29 33rd Swedish 1993 © John Scholes jscholes@kalva.demon.co.uk 16 January 2004 Last corrected/updated 16 Jan 04