Difference between revisions of "1967 IMO Problems/Problem 6"
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| − | In a sports contest, there were m medals awarded on n successive days (n > | + | In a sports contest, there were <math>m</math> medals awarded on <math>n</math> successive days <math>(n > |
| − | 1). On the first day, one medal and 1/ | + | 1)</math>. On the first day, one medal and <math>\frac{1}{7}</math> of the remaining <math>m - 1</math> medals |
| − | were awarded. On the second day, two medals and 1/ | + | were awarded. On the second day, two medals and <math>\frac{1}{7}</math> of the now remaining |
| − | medals were awarded; and so on. On the n-th and last day, the remaining n | + | medals were awarded; and so on. On the n-th and last day, the remaining <math>n</math> |
medals were awarded. How many days did the contest last, and how many | medals were awarded. How many days did the contest last, and how many | ||
medals were awarded altogether? | 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. | ||
| + | == See Also == {{IMO box|year=1967|num-b=5|after=Last Question}} | ||
Latest revision as of 10:02, 3 June 2021
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
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.
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 | ||
