Solution:

( Có bao nhiêu cặp ô vuông đơn vị trong bảng 3x6 sao cho chúng không có điểm chung ? ) 

When the two selected unit squares are on the same column, then one must be in the first row and the other in the third row. Therefore, there are 6 possible pairs.

When two unit squares selected are not in the same column, assume that one of the unit square is to the left of the other and below are the possible cases

(1) When the left unit square is located in the row 1

When the left unit square is on the 1^st column, the other unit square can be located in the 2^nd column of row 3 or on any unit square on the 3^rd, 4^th, 5^th and 6^th column. There are a total of 13 possible pairs. Likewise, when the unit squares located on any unit squares of other column. There are a total of 10 + 7 + 4 + 1 = 22 possible pairs

(2) The left unit square is located on row 2. When the left unit square is on the 1^st column, then the other unit square can be located on any other location of the 3^rd, 4^th, 5^th and 6^th There are a total of 12 possible pairs. Likewise, the unit square is located on any other column, there are a total of 9 + 6 + 3 = 18 possible pairs

(3) The left unit square is located on the 3^rd row. The situation is same as that of Case 1, we have a total of 13 + 22 = 35 possible pairs of unit squares

In summary, we have a total of 6 + 35 + 30 + 35 = 106 distinct pairs of unit square.