Three Dice

after Martin Gardner

Here is one mathematical trick based on a fact that the sum of the numbers on the opposite sides of a die is always seven. Turn round and ask somebody to throw three dice. Then ask him/her the next:
1) to add all the three numbers;
2) to take one die and add the number on the bottom face to the number he/she already counted;
3) to throw the same die again and add again the number it shows on top to the previous sum.
Now turn round telling your friends you can't know which die was thrown again. Take all the dice, shake them in your hand for a moment and then tell the correct sum. But how will you know that?