It is well-known that opposite sides of a classic hexahedral die add to 7. Given a vector of dice rolls, calculate the sum of the hidden face. That is, the sum of the values opposite the rolled value.
For example, if we roll a 2 and then a 6, we calculate that the opposite side of the dice were 5 and 1. Therefore, the answer is 6. This can also be calculated another way: since we know we rolled 2 dice, the total sum of the front and back faces of the dice must be 14 (7x2). If we then subtract the sum of the rolled values (2+6=8) from our total sum, we get the correct final answer (14-8=6)!