A cube has six different colored sides. Let's determine which side is opposite the brown side based on the given conditions.
- The red side is opposite to the black side.
- The green side is between the red and black sides.
- The blue side is adjacent to the white side.
- The brown side is adjacent to the blue side.
- The red side is face down.
Since the red side is face down and opposite to the black side, the black side must be on top. The green side must be on one of the lateral sides since it is between red and black.
Now, consider the blue and brown sides. The blue side must be adjacent to both the white and brown sides due to the adjacency requirements described. Therefore, blue cannot be on the top or bottom; it must be on one of the sides.
If red is down and black is up, the four lateral sides are green, blue, white, and brown. Since blue is adjacent to brown and white, it means blue and brown are on two adjacent lateral sides, leaving white as the side directly opposite to brown.
Conclusively, the side opposite the brown side is white.