### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

# Muggles Magic

##### Stage: 3 Challenge Level:

You can move the 4 pieces of this jigsaw around and fit them into the outlines shown below. Try for yourself with this interactivity. One square unit is missing in the lower shape.

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Explain what has happened to the missing area? (Of course muggles magic is not magic at all!)

Puzzles such as these first appeared in Zeitschrift für Mathematik und Physik Leipzig, 1868, vol XIII, page 162, although Martin Gardner states that Sam Lloyd the Elder, (there were two, father and son, who were both great puzzle producers and publishers in England) also talked about them around 1865. This particular one seems to have been invented by Roy Nauw of Kloetinge, from whom permission is being sought.