Puzzle 20: Democracy
The presidential elections are to be held in Anchuria. Of 20,000,000 voters only 1 percent (i.e. the regular army) support the current president Wobushko. He wants to be re-elected in a democratic way, which means the following. All voters are split into n1 groups, all of equal size. Then each group can be split into n2 smaller sub-groups of equal size, where n2 is the same for all groups. Then each subgroup is split into n3 equal sub-sub-groups, and so on. Each (sub)i-group chooses by majority rule one representative to represent it at level i-1, and so on. (If there is a tie, the opposition wins.) Can Wobushko organize the groups and distribute his supporters so that he wins the elections?