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Medals (Posted on 2004-01-29) Difficulty: 3 of 5
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?

See The Solution Submitted by Ravi Raja    
Rating: 3.2000 (5 votes)

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Solution my solution | Comment 3 of 5 |
on the last day n medals were given , said number being 6/7 of the number left day before after awarding n-1 medals( call it db)
n=6/7 *db
db=7/6*n so n is a multiple of 6: 6, 12, 18...
lets try the smallest one ( 6 awarded last day) and work our way backwards:

there were 6 days:

at the beginning of day 6 ..... 6 medals =6+0
at the beginning of day 6 .....12 medals=5+7
at the beginning of day 6 .....18 medals=4+14
at the beginning of day 6 .....24 medals=3+21
at the beginning of day 6 .....30 medals=2+28
at the beginning of day 6 .....36 medals=1+35

so: the answer is 36 medals awarded
during 6 days 6 each day

  Posted by Ady TZIDON on 2004-01-29 16:13:53
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