Question 1201527: Below is 4*4*4 cube. Matuk painted all six faces purple. when it dried he separated the small cubes and then glued the small cubes together with yellow glue to make a solid block. Before the glue dried he pushed out all the blocks which had purple paint on only one face. He pushed out from the front first. Then he pushed out the blocks from the side then the blocks form the top. How many cubes did he push out?
a)32 b) 24 c)64 d)48
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52780)   (Show Source):
You can put this solution on YOUR website! .
H I N T
The blocks that had purple paint on only one face,
are 2x2 = 4 blocks at EVERY face of the original 4x4-cube.
They are the blocks at every face that are not adjacent
the edges or the corners of the original 4x4-cube.
Therefore, to get the answer, you need to add 2x2 = 4 small blocks
as many times, as many faces you are interested in your exercise.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
OMG!!!
I am constantly astonished at how poorly written some of the math problems are that I see posted to this forum....
In this problem, when he separated the small cubes and then glued them together to form "a block", it does not say that that "block" was again a cube. And if it was a cube, it doesn't say that the small cubes were back in their original places, so we have no idea where the purple faces of the cubes are. And that of course makes it impossible to solve the problem, because we don't know which cubes to push.
So we have to ignore the significant shortcomings in the statement of the problem and assume that the reconstructed "block" was again a cube, with all the small cubes in their original places.
Given that, I interpret the problem differently than the other tutor.
When we push all the small cubes that show a purple face from the front, then from the side, and then from the top, we push out not only the 4 cubes in the center of each of the 6 faces; we also push out the 2x2x2 block of cubes that is the "center" of the 4x4x4 cube.
So the number of small cubes he pushed out is
6(4) + 2*2*2 = 24+8 = 32
ANSWER: a) 32
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