Stan likes music, and likes oldies the best. In his collection of music he has a cassette tape of “The Cassettes 20 Greatest Hits”. The amazing thing about the 20 Greatest Hits, is that each hit is exactly 3 minutes long. This fits perfectly on a 60-minute tape.

Songs 1 – 10 are on Side A, while 11 – 20 are on Side B. When listening to the tape, Stan does one strange thing. He listens to the first 5 songs on side A, then flips it to the other side. He then listens to Side B from that point until the tape ends. How many songs does Stan hear?

• The tape is wrapped around two spools that have identical diameters of 1 cm.
• The spool that is receiving the tape rotates at a constant speed.
• The tape, when located all on one spool, measures 5 cm in diameter.

I think the key to this problem is in what assumptions are made about the definitions.  I'm assuming that the 60 minute tape is 30 minutes on side A and 30 minutes on side B.  If this is true then Stan will hear the first 5 side A songs followed by the last 5 side B songs for a total of 10 songs.

If the 60 minute tape has 60 minutes in each direction, then it depends on where Stan put all the songs in the first place.  If he used the first 30 minutes of side A then the last 30 minutes of side B, then the answer is the same.  If all 20 songs are on side A, then side B would be blank.  I suspect this is not the case since the problem states that the music "fits perfectly on a 60-minute tape".

So I'll say 10 songs is how many Stan hears, provided he has the volume turned up, is listening, has the speakers connected, and is not deaf.

Posted by Larry on 2004-04-27 15:15:58