MathDB

A cube with edge length

3

is divided into

27

unit cubes. The numbers

1, 2,\ldots ,27

are distributed arbitrarily over the unit cubes, with one number in each cube. We form the

27

possible row sums (there are nine such sums of three integers for each of the three directions parallel with the edges of the cube). At most how many of the

27

row sums can be odd?

Problem Statement