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

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Muggles Magic

Stage: 3 Challenge Level: Challenge Level:1

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.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.