What An Odd Cube!

Abstract

We propose a new puzzle: Label the eight vertices of a cube using distinct integers between 0 and 12 (both inclusive) such that the induced labeling of each edge, given by the sum of the labels of its end points, causes the 12 edges to be labeled with distinct odd numbers 1, 3, … 23. Any solution to the puzzle is called a super odd-sum labeling. We deftly discover all super odd-sum labeling of the cube.