MathDB

With six rods a piece like the one in the figure is constructed. The three outer rods are equal to each other. The three inner rods are equal to each other. You want to paint each rod a single color so that at each joining point, the three arriving rods have a different color. The rods can only be painted blue, white, red or green. In how many ways can the piece be painted? https://cdn.artofproblemsolving.com/attachments/1/1/91e6b388498613486477ab6b51735055e920cc.gif

Problem Statement