A dice is numbered from 1 to 6 in different ways. If 1 is opposite to 5 and 2…

2023

A dice is numbered from 1 to 6 in different ways.

If 1 is opposite to 5 and 2 is opposite to 3, then

  1. A.

    4 is adjacent to 3 and 6

  2. B.

    2 is adjacent to 4 and 6

  3. C.

    4 is adjacent to 5 and 6

  4. D.

    6 is adjacent to 3 and 4

Attempted by 2 students.

Show answer & explanation

Correct answer: B

On a standard six-faced die, every face has exactly one opposite face, and each face is adjacent to every other face except itself and its own opposite. So once two of the three opposite-face pairs among the six numbers are fixed, the two numbers left over automatically become the third opposite pair.

Here 1 is opposite 5 and 2 is opposite 3, which accounts for four of the six faces. The two remaining faces, 4 and 6, must therefore be opposite to each other.

Since 2's only opposite face is 3, 2 must be adjacent to every other face on the die, including 4 and 6.

This also confirms that 4 and 6, being opposite faces, cannot be adjacent to each other or to any option that pairs them together as neighbours.

So 2 is adjacent to 4 and 6.

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