IMO 1967 Problem B3 In a sports contest a total of m medals were awarded over n days. On the first day one medal and 1/7 of the remaining medals were awarded. On the second day two medals and 1/7 of the remaining medals were awarded, and so on. On the last day, the remaining n medals were awarded. How many medals were awarded, and over how many days?
Let the number of medals remaining at the start of day r be m r . Then m 1 = m, and 6(m k - k)/7 = m k+1 for k  n - 6, so n = 6 and m = 36. s are also available in: Samuel L Greitzer, International Mathematical Olympiads 1959-1977, MAA 1978, and in István Reiman, International Mathematical Olympiad 1959-1999, ISBN 189-8855-48- X. 9th IMO 1967 © John Scholes jscholes@kalva.demon.co.uk 29 Sep 1998 Last corrected/updated 29 Sep 1998