April wrote: Is it possible to build a $ 4\times 4\times4$ cube from blocks of the following shape consisting of $ 4$ unit cubes? It can be built, but it is a bit hard to explain how without opportunity to draw it. Just try it out yourself

Who can post the official solution ? Thanks.

Solution will goes this way: cover the whole cube in a chessboard fashion now as the tetramino covers up 2 black and 2 white cubes it must coverup the whole cube but i made a sketchup file showing that how 8 tetraminos fill up 2*4*4 cube .now it is easy to double that i hop eyou have google sketchup! what you have to do is: open my file and then view>animation>play my browser says"The extension skp is not allowed."so you have to download it from http://www.4shared.com/file/PxYZUl2Z/cube_revisted.html but i have a doubt that what the condition that the tetraminoes will fill up a m*n*p cube? can anybuddy generalise>?

ACTUALLY i am too in doubt can any one please have a look http://www.artofproblemsolving.com/Forum/viewtopic.php?f=41&t=394305&p=2192229#p2192229

I suck at visualization but this seems to build a $2 \times 4 \times 4$. 1122 3114 3554 5566 ---- 7224 7784 3788 3668 EDIT in response: these are two layers of cubes, so you should imagine one 4x4 square on top of the other in 3D, and the cubes with the same number are part of the same tetromino.

math_explorer wrote: I suck at visualization but this seems to build a $2 \times 4 \times 4$. 1122 3114 3554 5566 ---- 7224 7784 3788 3668 srrry dude can u please explain me these code arrangement? how u create this?

Same numbers are parts of the same tetromino. They are two adjacent layers. How did he create that? Use the [ code ][/ code ] tags (without the spaces).

chaotic_iak wrote: Same numbers are parts of the same tetromino. They are two adjacent layers. thanks dude i was looking for this!!