MathDB

On a

50 \times 50

chessboard, we put, in the lower left corner, a die whose faces are numbered from

1

6

. By convention, the sum of digits on two opposite side of the die equals

7

. Adama wants to move the die to the diagonally opposite corner using the following rule: at each step, Adama can roll the die only on to its right side, or to its top side. We suppose that whenever the die lands on a square, the number on its bottom face is printed on the square. By the end of these operations, Adama wants to find the sum of the

99

numbers appearing on the chessboard. What are the maximum and minimum possible values of this sum?

Problem Statement