MathDB

C2

Part of 2017 Pan-African Shortlist

Problems(1)

PAMO 2017 Shortlist: Extrema of sum of numbers on a chessboard

Source: 2017 Pan-African Shortlist - C2

5/5/2019
On a 50×5050 \times 50 chessboard, we put, in the lower left corner, a die whose faces are numbered from 11 to 66. By convention, the sum of digits on two opposite side of the die equals 77. 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 9999 numbers appearing on the chessboard. What are the maximum and minimum possible values of this sum?
combinatorics