A cube with edge length 3 is divided into 27 unit cubes. The numbers 1,2,…,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? geometry3D geometrycombinatorics proposedcombinatorics