2. Genghis Khan organized his men into groups of 10 soldiers under a "leader of 10". Ten "leaders of 10" were under a "leader of 100". Ten "leader of 100" were under a "leader of 1,000". (a) If Khan had an army of 10,000 soldiers at the lowest level, how many men in total were under him in his organization? (b) If Khan had an army of 5,763 soldiers at the lowest level, how many men in total were under him in his organization? Assume that the groups of 10 should contain 1- if possible, but that a single group at each level may need to contain fewer men. 3. In the bible, Exodus chapter 18 describes how Moses was overwhelmed as the single judge of Israel because of the large number of trivial cases that were brought before him. His faster-in-law, Jethro, recommended a hierarchical system of appellate courts where the lowest-level judge had responsibility of 10 citizens. five judges of 10 sent the difficult cases that they could not resolve to a judge of 50 citizens. Two judges of 50 were under a judge of 100, and 10 judges of 100 were under a judge of 1,000. The judges of 1,000 citizens reported to Moses, who had to decide only the most difficult cases. (a) If the population were exactly 2,000 citizens (excluding judges), draw the three top levels of the hierarchy diagram. 4. A full binary tree is a tree whose leaves are all at the same level, and every node that is not a leaf has exactly two nodes under it. Figure 1.26 (page 28 of text) is a full binary tree with three levels. (a) Draw the full binary tree with four levels. (b) How many nodes total are in a full binary tree with five levels? (c) With six levels? (d) with n levels (as a general expression)?