A cube has six numbers marked 1, 2, 3, 4, 5 and 6 on its faces. Three views of the cube are shown below:

Correct Option

The numbers 2 and 3 can exist on faces (A) and (B), respectively.

Based on the initial three views of the cube, the opposite faces can be determined through logical deduction:

• Comparing View 1 (showing faces 1, 2, 3) and View 3 (showing faces 1, 5, 4), with '1' as the common face, a systematic rotation reveals the following relationships:
  • Face 2 is opposite Face 5.
  • Face 3 is opposite Face 4.
• Consequently, the remaining two numbers, 1 and 6, must be opposite each other.

Thus, the established pairs of opposite faces are: (1, 6), (2, 5), and (3, 4).

In the target view, the visible faces are 6, (A), and (B). A fundamental principle of a standard cube is that opposite faces cannot be simultaneously visible in any single perspective.

• Since face 6 is visible, its opposite face, 1, cannot be present on either face (A) or face (B).
• The remaining available numbers for faces (A) and (B) are 2, 3, 4, and 5 (excluding 1 and 6).
• Additionally, faces (A) and (B) must not be opposite to each other.
• If face (A) is 2 and face (B) is 3:
  • Neither 2 nor 3 is opposite to 6.
  • Faces 2 and 3 are not opposite to each other (2 is opposite 5, and 3 is opposite 4).
  • This combination is consistent with all established rules and relationships for a standard cube.

Incorrect Options

• Option 2 (6 and 1): This option is incorrect. Firstly, the number 6 is already visible on one face of the cube; therefore, face (A) cannot also be 6. Secondly, 6 and 1 are opposite faces, and opposite faces cannot be simultaneously visible on a single view of the cube.

• Option 3 (1 and 4): This option is incorrect because 6 and 1 are opposite faces. Since 6 is already visible in the given view, its opposite face, 1, cannot be visible on face (A).

• Option 4 (3 and 1): This option is incorrect because 6 and 1 are opposite faces. Since 6 is already visible in the given view, its opposite face, 1, cannot be visible on face (B).