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BMAT 2012 · Question 31 · Optimisation

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In each round of a competition the competitor who performed best in that round is awarded 6 points. The next best competitor gets 3 points and the third gets 1 point. There are four competitors, so the last player does not score any points. After 10 rounds the scores are totalled. After nine rounds had been completed, Jill knew that, regardless of the outcome of the final round there would be no ties and she would finish in third place. She also knew that whoever finished ahead out of Karen and Gemma would be the overall winner.

What is the highest score that the last placed player could finish with after all ten rounds are played?