Given below are pictures of a dice.
Which number is on the face opposite to 3?
Show Hint
In dice problems, if a face is seen with four different faces across multiple views, those four faces are adjacent to it.
The only remaining face is its opposite face.
Step 1: Observe Dice I.
The visible faces are:
\[
1,\;2,\;3
\]
Hence face \(3\) is adjacent to:
\[
1 \text{ and } 2
\]
Step 2: Observe Dice II.
The visible faces are:
\[
4,\;3,\;5
\]
Hence face \(3\) is adjacent to:
\[
4 \text{ and } 5
\]
Step 3: List all faces adjacent to 3.
Combining the information from Dice I and Dice II:
\[
3 \text{ is adjacent to } 1,2,4,5
\]
Thus the four adjacent faces of \(3\) are:
\[
{1,\;2,\;4,\;5}
\]
Step 4: Use the cube property.
A face of a cube has exactly four adjacent faces and one opposite face.
The six faces of the dice are:
\[
1,\;2,\;3,\;4,\;5,\;6
\]
Among these,
\[
1,\;2,\;4,\;5
\]
are already adjacent to \(3\).
The only number remaining is:
\[
6
\]
Therefore \(6\) must be opposite to \(3\).
Step 5: Write the final answer.
\[
{6}
\]
Hence option (A) is correct.
