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.


1 Answer 1


The large block will have an $8\times 8$ face. It must break down into $2\times3$ and $3\times3$ faces. So each small face has area divisible by $3$, yet the total area of that face, $64$, is not divisible by $3$.

So it cannot be done.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.