Question

A die is numbered from $1$ to $6$ in different ways. If $1$ is adjacent to $2,$ $3$ and $5,$ then which of the following statements is necessarily true?

• A. $1$ is adjacent to $4$
• B. $2$ is adjacent to $5$
• C. $1$ is adjacent to $6$
• D. $4$ is adjacent to $6$

Answer 1

The correct option is D $4$ is adjacent to $6$

If $1$ is adjacent to $2,3$ and $5,$ then there is a possibility that numbers $6$ or $4$ has to be opposite to $1.$
Hence, options $A$ and $C$ are definitely not possible.
The number $2$ need not necessarily be adjacent to $5.$
In a six-faced die, for a particular face, there is one opposite face and four adjacent faces. Therefore $4$ will definitely be adjacent to $6.$
Hence, option $D$ is correct.