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Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

Always Perfect

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Have you tried some simple cases to see if there is a pattern?

If you have a number "$x$" the next number is "$x +1$". How could you write four consecutive numbers?

If you can express $x^4 + \ldots + 16$ as a perfect square, the two factors will be of the form $(x^2 +\ldots + 4)$.


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.