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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?

Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Bull's Eye

What fractions of the largest circle are the two shaded regions?

Blue and White

Age 11 to 14 Challenge Level:

In the examples below identical squares of side one unit contain some circles shaded blue.
 


In which of the four examples is the shaded area greatest?

 

This problem is also available in French: Bleu et Blanc
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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