A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted? Choose the correct choice from the following options:  A) 3  B) 6  C) 8  D) 12  E) 27
There are 4 adjacent sides for every face of the cube.   Let's say side 1 is painted red, then the 4 adjacent sides can be either green or blue alternating. This can be done in 2 ways.   GBGB   BGBG   Sixth side should be the same color as side 1.   For each color chosen for side 1(and side6) there are 2 ways of painting side 2,3,4 and 5.   No. of colors that can be chosen for side 1(and side6) is 3.   So 3*2 = 6..   ANSWER:6
<result>B</result>
A cube marked 1, 2, 3, 4, 5, and 6 on its six faces. Three colors, red, blue, and green are used to paint the six faces of the cube. If the adjacent faces are painted with the different colors, in how many ways can the cube be painted?