Let the coordinates of (infinite-dimensional) Hilbert space H be denoted as x_1, x_2, x_3, ..., x_n, .... Note that the integer points of H correspond to arbitrary sequences of integers *only finitely many of which* are non-zero. The cubic tiling of H has one cube for each integer point of H. Definition: ----------- The cube at the integer point x is "adjacent" to the cube at the integer point y exactly if y differs from x in precisely one coordinate, by the amount ±1 in that coordinate, and has all the other coordinates equal to those of x. Puzzle: ------- Prove that given infinitely many colors, indexed by the set of integers, the cubes of the cubic tiling of H can be colored so that each cube is adjacent to exactly one cube of each other color (and not adjacent to any cube of its own color). —Dan