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### Number and algebra

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# Painted Cube

How many vertices, faces and edges are there in a cube?

Where are the cubes with no faces painted?

Where are the cubes with 1, 2, 3, 4, 5, 6 faces painted?

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How many vertices, faces and edges are there in a cube?

Where are the cubes with no faces painted?

Where are the cubes with 1, 2, 3, 4, 5, 6 faces painted?

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?

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