Problem: a cube is divided into 512 identical cubelets . each cut is made parallel to some surface of the cube . but before doing that , the cube is painted with green on one set of opposite faces , red on another set of opposite faces , and blue on the third set of opposite faces . how many cubelets are painted with exactly one colour ?
Rationale: "each face of the cube has 8 x 8 = 64 cubelets . on each face , only the interior cubelets are painted one colour . on each side , 6 x 6 = 36 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 36 = 216 the answer is a ."
annotated_formula: divide(subtract(512, multiply(multiply(const_4, const_2), const_3)), const_2)