Question 6
In a sports competition lasting $n$ days there are $m$ medals to be won. On the first day, one medal and $1/7$ of the remaining $m-1$ medals are won. On the second day, $2$ medals and $1/7$ of the remainder are won. And so on. On the $n$th day exactly $n$ medals are won. How many days did the competition last and what was the total number of medals?