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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?

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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?

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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?

Hex

Stage: 3 Challenge Level: Challenge Level:1
If the original hexagon has sides of length 3 units what is the length of the sides of the smaller hexagons?
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.