In a sports competition, there were M medals awarded on N successive days, where N is greater than 1.

• On the first day: 1 Medal and 1/9 of the remaining (M-1) medals were awarded.
• On the second day: 2 Medals and 1/9 of the now remaining medals were awarded, ...and, so on.
• On the Nth and the last day: the remaining N medals were awarded.

How many days did the contest last and how many medals were awarded altogether?
Provide valid reasoning for your answers.