Question 1
Faces of identical dice are labeled by digits 1, 2, 3, 4, 5 and 6. The digit 1 is opposite the digit 6, the digit 2 is opposite the digit 5, and the digit 3 is opposite digit 4. A three-dimensional shape can be formed by putting together a number of these dice in such a way that only two faces with the same digits are glued. Two dice can be put together either horizontally or vertically. After putting the dice together, the digits on the glued faces cannot be seen anymore. If we put the shape on the floor, the digits on the bottom faces cannot be seen as well. In the figure below we see two examples of the shapes.
Questions:
(a) Construct a shape by putting together three dice, then place it on the floor so that the sum of the visible digits on the side and the top faces of the shape is minimum.
(b) Construct a shape by putting together four dice, then place it on the floor so that the sum of the visible digits on the side and the top faces of the shape is minimum.
Questions:
(a) Construct a shape by putting together three dice, then place it on the floor so that the sum of the visible digits on the side and the top faces of the shape is minimum.
(b) Construct a shape by putting together four dice, then place it on the floor so that the sum of the visible digits on the side and the top faces of the shape is minimum.