**(1,2,3…11,12)**.

Partition it into 3 subsets, each with a distinct number of members ,

e.g .

**A=(1,2); B=(3,5,11,12) & C=(4,6,7,8,9,10)**.

Evaluate the sums of the members for each of the subsets, in our example:

**S**

_{a}=3 ; S_{b}=31 & S_{c}=44;Now evaluate:

F1 (product of the three sums) =

**S**in our example.

_{a}* S_{b}* S_{c}, i.e. 3*31*44 = 4092F2= S

_{a}* S

_{b}+ S

_{c}; equals to

**93+44=137**in our case.

F3= d(S

_{a}) +d(S

_{b}) + d(S

_{c}); where d(N) is the number of N's divisors.

So in our case

**F3=2+2+6 = 10.**

The 3

**independent**tasks :

Executing the above procedures find the partitions of the main set, that provide maximum values for **F1, F2 & F3.**