Originally Posted by

**wonderboy1953** Let's say you have two rectangular pieces of cardboard 3 feet long. You lay down the first cardboard on a table and tape the second one so that the two short sides meet one another forming a cylinder.

Now lay down the cylinder where the lowest part meets the first cardboard piece from where it starts along the long side and roll the cylinder over to the other side (along the long, 3-foot side of the laid down cardboard piece). How far has the circumference of the cylinder moved and how many times has it rolled to get to the other side?

Take the first cardboard piece and tape up its two short sides to make another cylinder. Now roll the second cylinder around again back to its starting point. How long has the circumference rolled and how many time did it roll?

Now take the second cylinder and stand it up straight (the circular part) perpendicular to the first cylinder and repeat the rolling procedure around the circumference of the first cylinder and the same questions: how far has the circumference of the second cylinder rolled and how many times.

Repeat the rolls, but assume the second cylinder's circumference shrunk down to two feet. Now what happens? How about a foot?

(I don't know the answers myself and this was inspired by a puzzle I read quite a few moons ago - some of this I made up myself).