MathDB

In a

7\times 7\times 7

cube, the unit cubes are colored white, black and gray colors so that for any two colors the number of cubes of these two colors are different. In this case,

N

parallel rows of

7

cubes were found, each of which there are more white cubes than gray and than black. Likewise, there were

N

parallel rows of

7

cubes, each of which contained gray there are more cubes than white and than black, and there are also N parallel rows of

7

cubes, each of which contains more black cubes than white ones and than gray ones. What is the largest

N

for which this is possible?

Problem Statement