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'An Appearing Act' printed from http://nrich.maths.org/
You may wish to print out some dotty paper.
Take an 8 by 8 square, and cut it up like this:
Rearrange the pieces to make a 13 by 5 rectangle:
It seems we can use the same pieces to make two shapes with different areas!
Can you explain why?
Can you perform this “magic trick” by splitting squares of other sizes in a similar way?
Which squares are least obvious?
What patterns are there in the square sizes?