10 pieces of dice are piled up on the desk so that the direction of each face might become same as shown in the figure below.
Find the total of the number of dice spots not to be seen from anywhere.
Answer
120
Solution
The number of face of each die is six.
Total number of faces of 10 dice is 6 × 10 = 60.
The number of faces can be seen is (1 + 2 + 3) × 5 = 30.
The number of faces being attached on the desk is six.
The number of points where the face of dice are attached each other is (30 - 6) / 2 = 12.
Therefore the total of the number of dice spots not to be seen from anywhere is 7 × 12 + 6 × 6 = 120.
