Enigma 1322: Geometric runs
From New Scientist #2481, 8th January 2005
In cross-country races with teams of six runners, the team scores are calculated by adding together the finishing positions of the first four runners in each team, the lowest-scoring team being the winner. Individuals never tie for any position.
The fifth and sixth runners to finish in each team do not contribute to the team score, but if they finish ahead of scoring runners in other teams they make the positions of those runners and their teams’ scores that much worse.
In a race involving seven teams of six runners, the scores of the first four teams formed a geometric progression, as did the scores of the last four teams.
What were the scores of the first and last teams?
This puzzle completes the archive of Enigmas from the beginning of 2005 up to the end of 2013 (and the end of Enigma), which is 459 puzzles. There are also 193 puzzles available from the start of Enigma (in 1979) to the beginning of 1983, which together with a random puzzle from 2000 currently makes up the 653 Enigma puzzles on the site.