A dice has its faces marked by numbers 10, 20, 30, 40, 50 and 60. Two positions of the same dice are given. In the first position, the visible faces are 60, 40, and 30. In the second position, the visible faces are 60, 10, and 20. Which face is opposite to face 50?

Let's find the face opposite to 50 by examining the two given orientations:Position 1 visible faces: 60, 40, 30Position 2 visible faces: 60, 10, 20The number 60 is the common face in both orientations. Writing the faces in a clockwise direction starting from 60 gives:Position 1 sequence: $60\to 40\to 30$ Position 2 sequence: $60\to 10\to 20$ Comparing the sequences:40 is opposite to 1030 is opposite to 20The only remaining unmarked face is 50, which must be opposite to the common face, 60.