Six numbers 21, 22, 23, 24, 25 and 26 are written on different faces of a dice. Three positions of this dice are shown in the figure. Find the number on the face opposite to 24.
Correct Answer :
21
Solution :
To find the number on the face opposite to 24, we can analyze the three given positions of the dice shown in the figure:
Step 1: Identify the visible faces in each position:
- Position 1: The visible faces are 21, 23, and 25.
- Position 2: The visible faces are 21, 25, and 22.
- Position 3: The visible faces are 25, 24, and 22.
Step 2: Determine which faces are adjacent to 25:
- From Position 1, we see that 21 and 23 are adjacent to 25.
- From Position 2, we see that 21 and 22 are adjacent to 25.
- From Position 3, we see that 24 and 22 are adjacent to 25.
Combining these observations, the faces adjacent to 25 are 21, 22, 23, and 24. Since a face on a dice can have at most 4 adjacent faces, the remaining face 26 must be opposite to 25.
Step 3: Analyze the transition between Position 2 and Position 3:
- In Position 2, 21 is on the top face, 25 is on the left face, and 22 is on the right face.
- In Position 3, 25 is on the top face, 24 is on the left face, and 22 is on the right face.
- By keeping the face with 22 on the right side and tilting the dice so that the face with 25 moves from the left to the top, the top face (21) moves to the opposite side of the current left face (24).
- Therefore, the face opposite to 24 is 21.
The correct answer is 21.
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