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1990 AHSME #9: Edges of a cube

Source:

January 1, 2013
geometry3D geometryAMC

Problem Statement

Each edge of a cube is colored either red or black. Every face of the cube has at least one black edge. The smallest possible number of black edges is
<spanclass=latexbold>(A)</span>2<spanclass=latexbold>(B)</span>3<spanclass=latexbold>(C)</span>4<spanclass=latexbold>(D)</span>5<spanclass=latexbold>(E)</span>6<span class='latex-bold'>(A) </span>2\qquad <span class='latex-bold'>(B) </span>3\qquad <span class='latex-bold'>(C) </span>4\qquad <span class='latex-bold'>(D) </span>5\qquad <span class='latex-bold'>(E) </span>6\qquad