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A cube has the dimension of 3x4x5. It is colored with three different colors namely red, green and black paint
A cube has the dimension of 3x4x5. It is colored with three different colors namely red, green and black painted on opposite corners of the cube. The cube is cut into 78 smaller cubes. 73 of them are smaller and 5 are bigger, but they have equal dimensions. Now, you need to calculate no. of cubes painted with red color, no. of cubes painted on three sides, no. of cubes painted on two sides, no. of cubes painted on one sides and no. of cubes painted without any painting.
For the pedants, let us say:
1. It is a rectangular prism.
2. Opposite faces are painted the same color.
3. The prism is cut into 73 equal-sized cubes plus 5 larger but also equal-sized cubes.
This seems like a really interesting problem. Wish I knew how to tackle it!
With some faddling about on paper, I got a good match for the cube sizes, with the smaller ones being 0.9 per side and the larger 1.107 per side (23% larger).
73 x 0.9^3 + 5 x 1.107^3 = 59.99999 = 3x4x5 = 60
This seems too close a match to be accidental, but is it physically possible to cut the prism into 78 cubes of the calculated sizes? That would seem to be important, but I don't see that it can be done!
So either I have the sizes wrong, or the sizes aren't important, and it is just the idea that the cutting that can be done that is important.
But it seems obvious that we have to know the disposition of each smaller cube (is it internal? in the corner? on an edge? on a face? totally internal?) to know how many faces are painted. So - what to do?
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