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Painted Faces

Stage: 2 Challenge Level: Challenge Level:1

Brian from Riverdale thought about the 3 by 3 by 3 cube carefully. He said:

There are 12 cubes that have only 2 faces painted. They are the middle cube along each edge.
They are red and yellow, red and blue, red and white, red and black, black and blue, black and yellow, black and green, green and white, green and blue, green and yellow, yellow and white, white and blue.

Rebecca from St John the Baptist School, Findon, explained how she went about the problem:

I found the answer by first drawing the cube on a piece of paper, then making it real in my head.
I then turned round the cube in my head and counted the squares that had two colours.

Well done, Rebecca! When you're picturing something in your head, as you were, we can also say you are "visualising". The Maths Group from Stourport Primary saw it in a slightly different, but equally good, way. They wrote:

Curt noticed that there are 4 of these little cubes on each of the 3 layers of the big cube.
Charlotte and Molly B. described where the 12 cubes are by imagining the big cube in 3 layers.
On the top and bottom layers the 4 cubes are on the outside of the face in between the 4 vertices making a cross shape pattern.
On the middle layer it is the 4 cubes on the outside corners.

Very well done. Has anybody investigated a 4 by 4 by 4 cube? Or even bigger cubes?

Let us know if you do.