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?

36 medals were awarded over a period of 6 days.

Proof:
1st Day: 36-1=35-(35*1/7)=35-5=30   6 medals were awarded
2nd Day: 30-2=28-(28*1/7)=28-4=24   6 medals were awarded
3rd Day: 24-3=21-(21*1/7)=21-3=18   6 medals were awarded
4th Day: 18-4=14-(14*1/7)=14-2=12   6 medals were awarded
5th Day: 12-5=7-(7*1/7)=7-1=6          6 medals were awarded
6th Day: 6-6=0-(0*1/7)=0-0=0            6 medals were awarded

(Note: Adding the bolded numbers in the left column will result in the bolded numbers in the right column.)

Posted by logischer Verstand on 2004-03-29 19:06:28