Suppose that the Tower of Hanois problem has five poles in a row. Disks can be transfered one by one from one pole to any other pole (there is no adjacency requirement), but at no time may a larger disk be palced on top of a smaller disk. Let tn be the minimum number of moves needed to transfer the entire tower of n disks from the left-most to the right-most pole. (a) Show that tn 2tn2 + 3, for n 3. (b) Give an example of n 3, where tn is not equal to 2tn2 + 3. Give the corresponding values of tn and tn2. (c) Show that tn 2tn3 + 5, for n 3.