3650.13 – A Solid Cube of Bricks?

Tags:Problem Set 18Pre-AlgebraAlgebra Prep

Can a solid cube 1 foot on a side be constructed from bricks measuring 2" x 4" x 8"? Explain your answer completely.


The cube has volume 123=172812^3 = 1728 cubic inches; a single brick has volume 2×4×8=642 \times 4 \times 8 = 64 cubic inches. As 6464 is a factor of 1728=64×271728 = 64 \times 27, the construction of the proposed cube is theoretically possible. It would use 27 bricks.

And that is as much as we currently know. Can you carry this further? Perhaps this problem calls for making a model!