You have an empty box which is a 11cm cube. You also have a supply of blocks. You have 54 2cm cubes, 24 3cm cubes and two 5cm cubes. Pack all 80 cubes into the box.
Nomenclature (x,y,z) = (left, bottom, front) corner of the cube to be placed.
5-cubes: (0,0,0), (6,6,6)
Put the 5 cubes in opposite corners
3-cubes: (5,0,0), (8,0,0), (5,3,0), (8,3,0),(5,6,0), (8,6,0), (0,5,0), (0,8,0), (0,5,3), (0,8,3), (5,6,3), (8,6,3)
The other twelve 3-cubes go in with the same relationship to the opposite 5-cube. (Subtract each coordinate from (8,8,8))
(0,2,5), (3,2,5), (8,0,5), (8,3,5), (0,2,8), (3,2,8), (0,5,8), (3,5,8), (0,8,8), (3,8,8), (8,0,8), (8,3,8)
The remainder is filled in with the 54 2-cubes, and a one cube void in the very center.
Solution
