As you may know, on a normal cubical die, the scores on opposite faces add up to 7.

Therefore, if you put a die on a table with the “1” face downwards, the sum of the scores on the visible faces will be 3 x 7 – 1 = 20, and this is the maximum possible value because only the “1” is not visible.

What is the maximum sum of the visible faces if you stack n dice on top of each other on a table to form a tower?

If you use 8 dice to make a 2 x 2 x 2 cube which sits on a table there will be a lot more faces that are no longer visible. What is the maximum sum of the visible faces now?

What is the maximum sum of the visible faces for a 3 x 3 x 3 cube on a table made using 27 normal dice? What about for a 4 x 4 x 4 cube? Or an n x n x n cube?