15 May '05 07:54

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

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