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Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Squares, Squares and More Squares

Age 11 to 14 Challenge Level:

Pattern of squares in squares

The diagram shows a square dissected into seven smaller squares.

Can a square be dissected into any number of squares?

Can you dissect a square into: two, three, four, five ... $n$ other squares?

Can you justify your findings?