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  • Early Years Foundation Stage

Platonic Planet

Age 14 to 16
Challenge Level Yellow starYellow starYellow star
  • Problem
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How much of the planet's surface can the alien see if she is in the middle of one of the faces?
What about on one of the edges?
Or at a vertex?

Try to picture a route around the planet either in three dimensions or on a net. Can you be sure every point on the surface is visible from your route? Can you make a more efficient route? Some diagrams might help!

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P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...

Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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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.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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