Crofter u know this?

[skillszone]

In a sports contest there were m medals awarded on n successive days (n > 1). On the first day 1 medal and 1/7 of the remaining m - 1 medals were awarded.
On the second day 2 medals and 1/7 of the now remaining medals was awarded; and so on.
On the nth and last day, the remaining n medals were awarded. How many days did the contest last, and how many medals were awarded altogether?

[crofter]

skillszone This is a much more challenging problem than those posed below. I'll try to work on it in the evening and come back to you.

Using the notatation M, L and k to denote Medals awarded, those Left and Day number, then
M(k) = k + 1/7* [L(k-1) -k]
and
L(k) = L(k-1) - M(k). This system of equations needs careful thought.

[Grace Digger]

36 medals over 6 days

[crofter]

Grace Thank you for saving me time messing about with my "equations". What a nice problem with such a neat solution!
I've noted your name in the past and shall look out for you in the future. A name to be reckoned with. Well done!

[Grace Digger]

Hi Crofter -- thanks for your nice words -- you only need to ask!!
I didn't want you to get too involved with all those equations. Now I'm retired, I've got plenty time to do the old fashioned trial and error approach.