MathDB

Consider cubes of edge length 5 composed of 125 cubes of edge length 1 where each of the 125 cubes is either coloured black or white. A cube of edge length 5 is called "big", a cube od edge length is called "small". A posititve integer

n

is called "representable" if there is a big cube with exactly

n

small cubes where each row of five small cubes has an even number of black cubes whose centres lie on a line with distances

1,2,3,4

(zero counts as even number). (a) What is the smallest and biggest representable number? (b) Construct 45 representable numbers.

Problem Statement