6.1. A cube lies on a plane. Each face is marked with 1 to 6 points such that the sum of points on opposite faces is always 7. The cube is rolled over the plane as shown in the picture. How many points will be on the top face of the cube when it lands on the last cell?

![](https://cdn.mathpix.com/cropped/2024_05_06_ffa720cb9bc207f8b509g-06.jpg?height=854&width=1816&top_left_y=284&top_left_x=217)
Answer: 5

Solution. To find out the answer, you need to imagine rolling the die in the opposite direction and each time keep track of where the face that will end up on top will be. It turns out that this face will be at the bottom in the initial position of the die. Since the top face has 2 dots, the bottom face now has 5 dots.