The set (1,2,3,4) can be partioned into two subsets (1,4) and (2,3) of the same size. 1+4=2+3

a)find the next whole number n, above 4, for which the set (1,2,...n) can be paritioned into two subsets S and T of the same size, with the sum of S and T the same.

b)find all partition in a) with the additional property that the sum of the squares of the numbers in S equals the sum of the squares of the numbers in T.

Terri says she can partition the set (1,2...16) into subsets S and T of the same size so that:

- the sum of the numbers in S equals the sum of T

-the sum of the squares of the number in S equals the sum of the squares of the numbers in T.

-the sum of the cubes of the numbers in S equals the sum of the cubes of the numbers in T.

c) show terri is right.

Willy says she can partition the set (1,2...8) into subsets S and T, not necessarily the same size so that:

- the sum of the numbers in S equals the sum of T

-the sum of the squares of the number in S equals the sum of the squares of the numbers in T.

-the sum of the cubes of the numbers in S equals the sum of the cubes of the numbers in T.

d)show why you dont belive willy