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Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Painting Cubes

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

Lesser Digits

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Colour Building

Age 11 to 14
Challenge Level

Is there a way to work systematically to make sure you have found all the possibilities?

When we make the length of the pink rod, how many possibilities have a red on the left?
How many possibilities have a white on the left?

Can you use this idea of thinking separately about the solutions that begin with a red, and the ones that begin with a white, to help you explain the patterns that you find?
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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NRICH is part of the family of activities in the Millennium Mathematics Project.