IT-CESENATICO 2005 Problem 3

In each cell of a $4 \times 4$ table a digit $1$ or $2$ 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.