Each of the six different faces of a cube has been coated with a different colour i.e., V, I, B, G, Y and O. Following information is given: 1) Colours Y, O and B are on adjacent faces. 2) Colours I, G and Y are on adjacent faces. 3) Colours B, G and Y are on adjacent faces. 4) Colours O, V and B are on adjacent faces. Which is the colour of the face opposite to the face coloured with O?

Here's a step-by-step analysis to determine the color opposite to O:

1. Identify all adjacencies for each color from the statements.

   • "Y, O and B are on adjacent faces" implies Y-O, O-B, B-Y.
   • "I, G and Y are on adjacent faces" implies I-G, G-Y, Y-I.
   • "B, G and Y are on adjacent faces" implies B-G, G-Y, Y-B. (This largely confirms adjacencies from previous statements).
   • "O, V and B are on adjacent faces" implies O-V, V-B, B-O.

   Consolidating the adjacencies for each color:

   • Y is adjacent to: O, B, I, G (from statements 1, 2, 3)
   • O is adjacent to: Y, B, V (from statements 1, 4)
   • B is adjacent to: Y, O, G, V (from statements 1, 3, 4)
   • I is adjacent to: G, Y (from statement 2)
   • G is adjacent to: I, Y, B (from statements 2, 3)
   • V is adjacent to: O, B (from statement 4)

2. Deduce opposite pairs. A cube face has exactly four adjacent faces. From the adjacencies of Y, we see Y is adjacent to O, B, I, and G. These are four distinct colors. Since there are six colors in total (V, I, B, G, Y, O), the fifth color, V, must be opposite to Y. Deduction 1: Y is opposite to V.

3. Place the colors to determine the opposite of O.

   • Let's assume Y is the Top face. Then V must be the Bottom face (from Deduction 1).
   • Now consider O. O is adjacent to Y (Top) and V (Bottom) (from its list of adjacencies). A face that is adjacent to both Top and Bottom must be a side face (Front, Back, Left, or Right). Let's place O as the Front face.
   • So far: Y (Top), V (Bottom), O (Front).
   • O (Front) is also adjacent to B (from its list of adjacencies). B must be one of the remaining side faces (Left or Right). Let's place B as the Right face.
   • So far: Y (Top), V (Bottom), O (Front), B (Right).
   • The remaining faces are Left and Back. The remaining colors are I and G.

4. Determine the positions of I and G.

   • From statement (2): "I, G and Y are on adjacent faces." This means I and G are adjacent to Y (Top), and I and G are adjacent to each other. The Left and Back faces are both adjacent to Top and are adjacent to each other, so this is consistent.
   • From statement (3): "B, G and Y are on adjacent faces." This means B (Right) is adjacent to G, and G is adjacent to Y (Top).
   • If G were the Left face, then B (Right) and G (Left) would be opposite faces, meaning they cannot be adjacent. This would contradict statement (3) (B, G, Y are adjacent).
   • Therefore, G cannot be the Left face. G must be the Back face.
   • If G is Back, then I must be Left.

5. Final Configuration and Verification.

   • Y = Top
   • V = Bottom
   • O = Front
   • B = Right
   • G = Back
   • I = Left

   Let's check all statements with this configuration:

   • 1. Y, O, B (Top, Front, Right) are adjacent: Yes, they meet at a corner.
   • 2. I, G, Y (Left, Back, Top) are adjacent: Yes, they meet at a corner.
   • 3. B, G, Y (Right, Back, Top) are adjacent: Yes, they meet at a corner.
   • 4. O, V, B (Front, Bottom, Right) are adjacent: Yes, they meet at a corner. All statements are consistent with this arrangement.

6. Answer the question. In this configuration, O (Front) is opposite to G (Back).

The final answer is C) G.