# Dice

#### absoluzation

The counting elf Zacharias owns a big red dice (the classical variant available all over the world). Its six faces show 1, 2, 3, 4, 5, 6 pips, respectively, and the numbers of pips on two opposite faces add up to the sum 7. Almost dozing off, Zacharias is sitting in front of a huge 101 x 101 chessboard, when he suddenly notices that the squares on the chessboard are precisely the same size as the faces of his dice. All at once, he is wide awake.
Zacharias places his dice onto the southwesternmost square of the chessboard and memorizes the number of pips on the top face of the dice. Then, he tilts the dice to the adjacent square in the north or to the adjacent square in the east and again memorizes the number of pips on the top face. He keeps tilting and tilting and tilting and tilting the dice—again and again—always to the adjacent square in the north or in the east, until the dice finally reaches the northeasternmost square on the chessboard. Now, Zacharias has altogether memorized 201 numbers of pips, and he writes the sum of these 201 numbers into his notebook.
Then, he repeats the entire procedure, and again writes the sum of the resulting 201 numbers into his notebook. In this way, Zacharias proceeds for several days, filling his notebook with hundreds of sums.
Our question: What is the largest possible number of different sums that may show up in Zacharias' notebook?

#### absoluzation

(The possibilities are 6, 10, 12, 24, 120, 216, 256, 720, 1006, 1206)