(a) At the J. & J. Chemical Company, Jeannette has received three shipments that contain a total of seven different chemicals. Furthermore, the nature of these chemicals is such that for all 1 ≤ i ≤ 5, chemical i cannot be stored in the same storage compartment as chemical i + 1 or chemical i + 2. Determine the smallest number of separate storage compartments that Jeannette will need to safely store these seven chemicals.
(b) Suppose that in addition to the conditions in part (a), the following four pairs of these same seven chemicals also require separate storage compartments: 1 and 4, 2 and 5, 2 and 6, and 3 and 6. What is the smallest number of storage compartments that Jeannette now needs to safely store the seven chemicals?