Vivek and Birthday Problem

How to approach this problem could you please give me kind off hint

@msid78641 hey here is hint:
For each pair p(a,b), we add a connection from a to b i.e. we insert ‘b’ to the node[a]. Thus if ‘a’ is selected ‘b’ would automatically be selected.
Now we take each node[i] and traverse through the connections till all the leaf nodes and count the total nodes directly/indirectly connected to that particular node[i].
We find that node[i] which has the minimum number of connections.