Problem 8

You select a set \(A=\{A_1,...,A_N\}\) of N different integers from the range 1 to 24. What is the minimum value of N such that for any choice of A there are two disjoint subsets of A with the same sum? Find also all selections A of size N-1 for which the sums of each subset are all different.

You should enter your answer in the form

N{selection 1}{selection 2} etc.

with no spaces, and where the selections are presented with the members in increasing numerical order. For example, if you think that the answer is 3 and your selections are {1,2} and {15,1} and {5,3} then you should enter

3{1,2}{1,15}{3,5}