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Painted cube investigation answers
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Painted cube investigation coursework 03
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Painted cube investigation coursework 04
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Painted cube investigation coursework 06
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Painted cube investigation coursework 07
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How many full-grown cubes did you use?
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Painted cube investigation coursework 08
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What happens if you paint a cube without paint?
If you do it with a 4 by 4 by 4 cube, you will end up with a 2 by 2 by 2 cube left without paint and if you do it with a 5 by 5 by 5 cube you will end up with a 3 by 3 by 3 cube without paint. Chantell, Billy, Connor and Chanel sent us this clear table summarising their findings. Rajeev sent us a very similar table of results.
How many Red Faces in a painted cube?
4) 3 red faces always got to be eight because these are corners (unless your cube is 1x1x1) Joe, Derek and Alice completed the table of results: NB. The values for n are correct unless n = 1. When n = 1 the single cube will have no red faces.
Why do you have to square a painted cube?
This is because the cubes in the centre remain clean, so you must take one off either edge and then cube it. This is because there are 6 faces to the cube, and only the ones not on the edge remain clean on 5 sides. So you must take one off either edge, then square it, then multiply it by the 6 faces.
How to calculate the number of painted cubes?
In her conclusion Alice added that in the second column the numbers were all cubic numbers, in the third column square numbers times 6 and in the fourth column multiples of 12. Belky explained how she reached her results. This is how she arrived at a formula for the number of cubes with two faces painted :
Last Update: Oct 2021
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