This problem is partly an exercise in careful reading. Not an easy problem. Each element of nonempty set A is a set of four distinct random digits; each digit is in range 1.9 (inclusive). Example: A 2, 4,7,5, , 4, 8, 3,,3,5,911. Construct set B from A as follows. For each element of A (that element is a set of four single-digit numbers), construct the corresponding element of B as the sum of the 24 four-digit integers that are all of the possible permutations of that element of A. So if A is a set of k sets, B is a set of k numbers. Find (and show how you get it) the smallest value of the GCD (greatest common divisor) of all of the elements of all possible instances of B. Note that the GCD of the elements in a particular set B depends on which sets are in the particular A from which B is derived. So we are looking for min(Iged(B): B is the set of the sums of all permutations derived frkn each of 4-element sets in A)). where the minimum is taken over all A's which are nonempty sets of 4-element sets as described above. Note: If the answer to this problem is a number S, there are two things to show 1. S is a factor of every GCD that cones from every set A A brief mathematical argument is needed for this part. 2. That there actually is a specific set A that leads to S as the GCD Show me such an A (there are many possibilities)