6. Give a proof of each of the following: (a) If the integers 1, 2, 3, ..., 7, are placed around a circle, in any order, then there exist two adjacent integers that have a sum greater than or equal to 9 . (b) If the integers 1, 2, 3, ..., 16 are placed around a circle, in any order, then there exist three integers in consecutive locations around the circle that have a sum greater than or equal to 27