In Eulers solution to the Konigsberg Bridge Problem, he observed that if there was a route that crossed each bridge exactly once, then this route could be represented by a sequence of eight letters, each of which is one of the four land regions A, B, C, and D shown in Figure 3.1. Show that it is impossible for any of these letters to appear only among the middle six terms of the sequence. What conclusion can be made from this observation?