You have a 3x3x3 cube, built with 1x1x1 bricks (27 bricks in total).

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The discussion centers on the challenge of constructing a 3x3x3 cube from 1x1x1 bricks after removing two diagonally opposite bricks. Participants confirm that this task is trivial for odd-dimension cubes, such as the 3x3x3, but becomes complex for even-dimension cubes like the 4x4x4. The removal of bricks must be understood in terms of their placement within the cube's planes, affecting the feasibility of reconstruction. The conversation highlights the inherent difficulties in solving such geometric puzzles, particularly in higher dimensions.

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You have a 3x3x3 cube, built with 1x1x1 bricks (27 bricks in total). You remove two diagonally opposite bricks (long diagonals). Can you build the remaining figure from 2xx1x1 bricks?
 
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i'm going to say:
no
the shapes volume is now 25 bricks
this would take 25 1x1x1 bricks
or 12.5 2x1x1 bricks
unless your allowed to have half a 2x1x1 brick, you can't do it?
unless I've missed something
 


Yeah, this problem becomes trivial if you've got an odd-dimension cube. However, it may still be impossible if it's a 4x4x4 cube, for different reasons, which I think is what the OP was going for. Just have to imply a different meaning of "Long Diagonal"-- that is, instead, you want to remove 2 cubes diagonally opposite on the same "plane" of the cube.

DaveE
 


Dave is right, I didn't realize the triviality of an odd-order cube :redface:

Still though, like he pointed out, the 4x4x4 case, or any order for that matter, is impossible too. But the solution (at least the one I know) is much harder!
 


There is a problem in dimension with its first digit. So, i am not guessing answer about this bricks game.
 

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