1967 IMO Problems/Problem 6

In a sports contest, there were $m$ medals awarded on $n$ successive days $(n > 1)$ . On the first day, one medal and $\frac{1}{7}$ of the remaining $m - 1$ medals were awarded. On the second day, two medals and $\frac{1}{7}$ of the now remaining medals were awarded; and so on. On the n-th and last day, the remaining $n$ medals were awarded. How many days did the contest last, and how many medals were awarded altogether?

Solution

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.

1967 IMO (Problems) • Resources
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1967 IMO Problems/Problem 6

Solution

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