A certain number of cubes are painted in six colours, each cube having six faces of different colours (the colours in different cubes may be arranged differently) . The cubes are placed on a table so as to form a rectangle. We are allowed to take out any column of cubes, rotate it (as a whole) along its long axis and replace it in the rectangle. A similar operation with rows is also allowed. Can we always make the rectangle monochromatic (i.e. such that the
top faces of all the cubes are the same colour) by means of such operations? ( D. Fomin , Leningrad)
Coloringcombinatorial geometrycombinatoricscuberectangle