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Trice

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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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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Marbles in a Box

How many winning lines can you make in a three-dimensional version of noughts and crosses?

Multiplication Cube

Age 11 to 14 Short Challenge Level:

If the figure shown is folded to form a cube then three faces meet at every vertex.

The numbers on the three faces meeting at any
vertex can be multiplied together.

What is the largest such product for the vertices of the cube?



This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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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