Imagine a rectangular piece of paper with several shapes drawn along the midline. Cut the paper into two and then cut the upper portion so that it becomes possible to exchange its two pieces. After the exchange there appear to be 1 shape less than before. This is in the spirit of the famous Sam Loyd's puzzle Disappearing Leprechauns.
The applet below is a much simplified version of Sam Loyd's invention. Both upper and lower portion could be dragged left or right and the number of shapes could be determined by clicking on the bold number at the bottom left of the applet.
(Tony Fatseas offers a beautiful replica of the original Sam Loyd's "Get Off the Earth" puzzle.)