Comments
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There seems to be a typo on the contests page; the contest tomorrow is named "2015-2016 ..." instead of "2016-2017 ...".
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I wanted to solve the problem described by this article (the problem makers cannot always sort problems by difficulty) and the problem described by vexorian (a problem solved by 86 people, another by 15 people and both with the same score) with the simplest algorithm. It is not the best one (a continous function would be best), but it is better than the method described in this article.
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How about assigning 500 points to the most solved problem, 1000 to the next one, 1500 to the next one ... 2500 to the least solved problem? In case of a tie you can assign the same score to tied problems.