Question

The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto. For how many years could this policy be continued before exactly the same program would have to be repeated?

Answer 1

3.945 years

Explanation:

To answer this problem, one must know that Beethoven has composed 32 piano sonatas, 9 symphonies and 5 piano concertos.

The number of different arrangements that can be made by playing a sonata, then a symphony and then a piano concerto is:

`n=32*9*5=1,440`

If a year has 365 days, the number of years that this daily policy could be continued before exactly the same program would have to be repeated is:

`y=(1,440)/(365)=3.945\ years`