Is it possible to build a $8×8×9$ block using $32$ bricks of dimensions $2×3×3$?
I tried to show that $8×8×9$ block can't contain $32$ blocks of dimensions $2×3×3$ . For that I tried to colour $1×1×1$ cubes.
(It would give me something like dominoes on chessboard where you can't use $1$ cell so blacks are more than whites , but domino covers the same number of blacks and whites)
I thought that I have to colour them in $18$ colours , but that's too much , and impossible to visualise in three-dimensional space.