Question

Each entry of a 4 × 4 square table of numbers is either 1 or 2. Suppose that the sum of 9
entries in each of the four 3 × 3 sub-square tables is divisible by 4, while the sum of all the
16 entries in the table is not divisible by 4. Determine the least and greatest possible values
of the sum of all the entries.

Answer 1

Divisible by four are 4,8, 12, and 16
a 3X3 square adds to at least 9. So each 3X3 square adds up to 12 or 16

Answer 2

Except that all the numbers now add up to 28 which is divisible by 4