We know that each row, column or 3x3 zone must contain all the digits 1 through 9 exactly once.

Now, 1+2+3+4+5+6+7+8+9=45 and this gives us a very important rule to remember:

The sum of all digits in a row, or a column, or a zone, is always 45.

Consider the zone shown to the right. The eight squares shaded pink add up to 5+15+14+7 = 41. Since all nine in the zone add up to 45, the ninth cell, shaded yellow, must be (45-41) = 4!