# [SOLVED] counting problem - programs for radio station

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• Sep 5th 2009, 08:44 PM
yvonnehr
[SOLVED] counting problem - programs for radio station
Can someone tell me if my solution is correct? There is a different answer in the book.
Thanks!
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Beethoven wrote 9 symphonies, and Mozart 27 piano concerts.

A station manager decides that on each successive night (7 days per week), a Beethoven symphony will be played, followed by a Mozart piano concerto, followed by a Schubert string quartet (of which there are 15). For roughly how many years could this policy be continued before exactly the same program would have to be repeated?

MY SOLUTION
B=9, M=27, Q=27
Using the Multiplication Priniciple
BxMxQ = 9x27x15 = 3645 3-day sequences,
i.e. 3645 sets consisting of 3 days each.

3645 sets x 3 days each set = 10935 days

10935 / 365 days in a year = 29.95 years or approximately 30 years of non-repeating 3 day sequences.
• Sep 6th 2009, 12:37 AM
BobP
Why a three day sequence ?
Aren't the three pieces played on the same night ?
• Sep 6th 2009, 08:38 AM
yvonnehr
You're right.
Quote:

Originally Posted by BobP
Why a three day sequence ?
Aren't the three pieces played on the same night ?

You are right. So the answer is 3654 days. Thanks.