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.

(In reply to the real solution by brad)

Yes, but if you read the previous comments you'll find that the tape moves faster as the side progresses, since the uptake spool is getting wider.

This means that three minutes towards the end takes up more of the spool than three minutes at the begining.

When you flip it, the uptake spool is small again, so the tape starts going more slowly past the head. This means that the first song on Side B takes up less taoe than the last song on Side A.

Posted by Sam on 2004-04-28 01:59:32