Sum of Squares

Place a digit (0 to 9) in each of the 16 cells of the 4×4 grid above.

• Reading across, each row forms a 4-digit number (leading zeros are allowed, so 0480 is the number 480). From top to bottom, the four rows must be divisible by 3, 4, 5 and 6 respectively.
• Reading down, each column forms a 4-digit number (the top cell is the thousands digit). From left to right, the four columns must be divisible by 7, 8, 9 and 11 respectively.

Your goal is to make the sum of the 16 digits as large as possible.

The grid that achieves the largest possible digit sum is unique.

Question. Give two numbers, separated by a comma: the largest possible digit sum, and the sum of the four row numbers (each row read left to right as a 4-digit number) in the grid that achieves it.