MathDB

In each cell of a

4 \times 4

table a digit

1

2

is written. Suppose that the sum of the digits in each of the four

3 \times 3

sub-tables is divisible by

4

, but the sum of the digits in the entire table is not divisible by

4

. Find the greatest and the smallest possible value of the sum of the

16

digits.

Problem Statement