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?
Solution
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See Also
| 1967 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Question |
| All IMO Problems and Solutions | ||
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.
