Question 30
An elastic band is wound around a deck of playing cards three times, making three horizontal stripes on top as shown on the left. Ignoring different ways the band can overlap itself, there are essentially two patterns on the underside, shown on the right. Treat two patterns as the same if one is a $180^\circ$ rotation of the other. How many different underside patterns are possible when the band is wound to make seven horizontal stripes on top?
