(a)  Consider all possible different decompositions of the number 18 into the product 
     of two whole numbers

         (1)  18 = 1*18

         (2)  18 = 2*9

         (3)  18 = 3*6

         (4)  18 = 6*3

         (5)  18 = 9*2

         (6)  18 = 18*1


     If you consider decompositions like (2) and (5) as different, 
     then the answer is "there are 6 different designs".

     If you consider decompositions like (2) and (5) as identical, 
     then the answer is "there are 3 different designs".


(b)  The same logic works in case (b).

     In this case, the number 41 is a prime number, so, the two possible answers are

         "there are two possible designs, if you consider the decompositions 

                  41 = 1*41
              and
                  41 = 41*1

          as different"

      or 

         "there is one possible design, if you consider the decompositions 

                  41 = 1*41
              and
                  41 = 41*1

          as identical".