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Square Pegs

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Not So Little X

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

Lying and Cheating

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

Square Areas

Age 11 to 14
Challenge Level

The outer square has sides of length 1.

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


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.
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