MathDB

The faces of a cube are painted in six different colors: red (R), white (W), green (G), brown (B), aqua (A), and purple (P). Three views of the cube are shown below. What is the color of the face opposite the aqua face?

\text{<span class='latex-bold'>(A) </span>red}\qquad \text{<span class='latex-bold'>(B) </span> white}\qquad\text{<span class='latex-bold'>(C) </span>green}\qquad\text{<span class='latex-bold'>(D) </span>brown }\qquad\text{<span class='latex-bold'>(E)</span> purple}

[asy] unitsize(2 cm);
pair x, y, z, trans; int i;
x = dir(-5); y = (0.6,0.5); z = (0,1); trans = (2,0);
for (i = 0; i <= 2; ++i) { draw(shift(i*trans)*((0,0)--x--(x + y)--(x + y + z)--(y + z)--z--cycle)); draw(shift(i*trans)*((x + z)--x)); draw(shift(i*trans)*((x + z)--(x + y + z))); draw(shift(i*trans)*((x + z)--z)); }
label(rotate(-3)*"

R

", (x + z)/2); label(rotate(-5)*slant(0.5)*"

B

", ((x + z) + (y + z))/2); label(rotate(35)*slant(0.5)*"

G

", ((x + z) + (x + y))/2);
label(rotate(-3)*"

W

", (x + z)/2 + trans); label(rotate(50)*slant(-1)*"

B

", ((x + z) + (y + z))/2 + trans); label(rotate(35)*slant(0.5)*"

R

", ((x + z) + (x + y))/2 + trans);
label(rotate(-3)*"

P

", (x + z)/2 + 2*trans); label(rotate(-5)*slant(0.5)*"

R

", ((x + z) + (y + z))/2 + 2*trans); label(rotate(-85)*slant(-1)*"

G

", ((x + z) + (x + y))/2 + 2*trans); [/asy]

Problem Statement