a        Show that you can divide the whole numbers from 1 to 48 into two groups (using all the numbers once each), so that the sum of the numbers in one group is equal to the sum of the numbers in the other group.

b       Show that you cannot divide the whole numbers from 1 to 50 into two groups, so that the sum of the numbers in one group is equal to the sum of the numbers in the other group.

c        Can you divide the whole numbers from 1 to 48 into two groups of equal size, so that the sum of the numbers in one group is equal to the sum of the numbers in the other group?

d       For which values of n can you divide the whole numbers from 1 to n into two groups so that the sum of the numbers in one group is equal to the sum of the numbers in the other group? For which of these values of n can you divide the whole numbers from 1 to n into two groups of equal size, so that the sum of the numbers in one group is equal to the sum of the numbers in the other group?