Problem Solving (PS) | A solid cube of side 6 is first painted pink and then cut into smaller

This question should be solved in two parts. First we need to find the number of cubes that can be cut out of the larger cube and then we need to find how many of these cubes thus cut out, form the middle part of the edge.

Moreover, let's note that the cube is painted OUTSIDE on all sides. Thus,

...the top and the adjoining sides are also painted pink, i.e, all 3 sides of the edge have been painted. We will call them the "corner blocks".
...there are blocks (ones that are not a part of any edge) that are only painted on one side. We will call them "interior blocks".
...there are blocks that are painted on only two sides (middle block of the edge). We will call them "middle-of-the-edge blocks".

For this question, we are only concerned with middle-of-the-edge blocks.

I) Since the larger cube has sides of length 6 and the smaller cube has side of length 2, the number of cubes that can be cut on each side is 6 / 2 = 3. This includes the edges being cut
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Statistics : Posted by youcouldsailaway • on 16 May 2016, 01:41 • Replies 3 • Views 22182

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