This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
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problem
Marbles in a box
How many winning lines can you make in a three-dimensional version of noughts and crosses?
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problem
Nine colours
Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
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problem
Triangles to tetrahedra
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
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problem
Tet-trouble
Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?
Image
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.