Two different positions of the same dice are described below. The faces are numbered from $1$ to $6$. In the first position, the numbers $1$, $2$, and $3$ are visible. In the second position, the numbers $1$, $5$, and $6$ are visible. Which number will be on the face opposite to the face showing $1$?

From the two given positions of the dice:
* In the first position, face $1$ is adjacent to faces $2$ and $3$.
* In the second position, face $1$ is adjacent to faces $5$ and $6$.

This means that face $1$ is adjacent to four faces: $2$, $3$, $5$, and $6$.
Since any face on a standard cube can have at most $4$ adjacent faces, the remaining unmentioned number must be directly opposite to it.

The missing number from the set $\{1,2,3,4,5,6\}$ is $4$.
Therefore, the face opposite to $1$ is $4$.