सहा पृष्ठांवर 1, 2, 3, 4, 5 आणि 6 संख्या असलेला सोबतचा घन अभ्यासा. 3 ही संख्या 1 किंवा 6 च्या विरुद्ध पृष्ठांवर नाही आणि 4 ही संख्या 6 च्या विरुद्ध पृष्ठावर नाही. जर 1 ही संख्या वरच्या पृष्ठावर राहील अशा रीतीने हा घन फिरवला आणि 6 संख्या असलेले उजवीकडचे पृष्ठ आताच्या 2 संख्या असलेल्या समोरच्या पृष्ठाच्या जागी आणले तर उजव्या पृष्ठावर कोणती संख्या असेल ?

The correct answer is Option C (3).

Key Points:
• Analysis of the Cube's Faces and Opposites:
• In the given initial view of the cube, face 1 is on top (Top), face 2 is on the front (Front), and face 6 is on the right (Right).
• Faces adjacent to 6 visible initially are 1 and 2. Thus, neither 1 nor 2 can be opposite to 6.
• The problem states: 3 is not opposite to 1 or 6, and 4 is not opposite to 6. Therefore, the face opposite to 6 cannot be 1, 2, 3, or 4. Hence, the face opposite to 6 must be 5.
• Now, we determine the opposite pairs. Since 3 is not opposite to 1 or 6, 3 must be opposite to 2 or 4. But since 2 is adjacent to 6 and 1, analyzing the cyclic arrangement: with 6 opposite to 5, the remaining faces around the vertical axis are 2, 6, opposite-to-2, and 5. With 3 not opposite to 1, the face opposite to 1 must be 4, which leaves 3 opposite to 2.
• Rotation of the Cube:
• The cube is rotated around the vertical axis keeping 1 on the Top face.
• The right face (which has number 6) is rotated 90° counter-clockwise (viewed from top) to take the Front position (replacing face 2).
• Consequently, the face that was originally on the back (opposite to 2) moves to the right side face.
• Since face 3 is opposite to face 2, moving face 6 to the front rotates face 3 directly onto the right face. Thus, the number on the right face will be 3.
• Revision Note:
• Deducing opposites (6↔5, 1↔4, 2↔3) shows rotating face 6 to the front brings the back face (3) to the right.