Enigma 1418: Non-scoring runners
24 June 2013
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From New Scientist #2578, 18th November 2006
In cross-country races, teams consist of six runners; team scores are calculated by adding together the finishing positions of the first four runners to finish in each team, the team with the lowest score winning. Individuals never tie. The fifth and sixth runners in each team do not score but if they finish ahead of scoring runners in other teams they make the positions of those runner and their teams’ scores worse.
In a race involving three teams, each of six runners, no two teams had the same score. The third team’s score was a multiple of the second team’s score, which itself was a multiple of the winning team’s score. The sum of the positions of the first three finishers in the winning team, the sum of the positions of the first two finishers in the second team and the position of the first finisher in the third team were identical.
What were the positions of the non-scoring runners in the second team?