Three positions of the same die are shown. What is the sum of the numbers on the three faces that are opposite the faces visible in position (iii)?

1 is seen with 2, 3, 6 and 5, so 1 is opposite 4. 2 is seen with 1, 3, 5 and 4, so 2 is opposite 6, leaving 3 opposite 5. Position (iii) shows 2, 5 and 4; their opposites are 6, 3 and 1: $6+3+1=10$. (11 is the sum of the visible faces themselves.)