1967 IMO Problems/Problem 6
In a sports contest, there were medals awarded on successive days . On the first day, one medal and of the remaining medals were awarded. On the second day, two medals and of the now remaining medals were awarded; and so on. On the n-th and last day, the remaining medals were awarded. How many days did the contest last, and how many medals were awarded altogether?
This is not a particularly elegant solution, but if you start from 1 and go all the way in a clever method, by only guessing those that are 1 more than a multiple of 7, you arrive at the answer of 36.
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