MathDB

With

150

white cubes of

1 \times 1 \times 1

a prism of

6 \times 5 \times 5

is assembled, its six faces are painted blue and then the prism is disassembled. Lucrecia must build a new prism, without holes, exclusively using cubes that have at least one blue face and so that the faces of Lucrecia's prism are all completely blue. Give the dimensions of the prism with the largest volume that Lucrecia can assemble.

Problem Statement