Get piece of paper in the shape of long rectangle. Draw the line along long side exactly in the middle of the rectangle. Then make Moebius strip from piece of paper. Finally cut it in the half - You will obtain two pieces of paper. Now make another Moebius strip but now, cut in in say 1/3 from the side along long side of the rectangle ( it is hard to describe as English is not my primary language ) . See what happen. You may ask people to guess before;-)
Do You know Steinhaus http://en.wikipedia.org/wiki/Hugo_Steinhaus book "Mathematical Kaleidoscope"? Read it and You will be ready for any occasion;-)
