Sir Alaric is the Keeper of the King's Record. In other words, he's a professional recorder in the days before computers. As such, his job is to keep track of how many hats multiply atop poor Bartholomew's head. Thanks to his efforts, we know the answer to be 500 and so can title the book properly. The ??? Hats of Bartholomew Cubbins just would not do.
The Captain of the King's Own Guard is the captain of the King's own… guard. Guess that's kind of a circular statement, huh? He tells the citizens of Didd to remove their hats for the King and later arrests Bartholomew on the King's orders. A loyal giver and follower of rules and orders this one.
Sir Snipps is the hat maker of the rich and famous. A tiny man, he sports scissors in lieu of a sword. As a master milliner extraordinaire, he thought he could easily remove Bartholomew's hat. Not so much.
Nadd is wise, the Father of Nadd is wiser, and the Father of the Father of Nadd is the wisest of the three. Though they sport fabulously wise beards, they can't figure out how to remove Bartholomew's hat.
These nine magicians sing magical charms with the aid of their black cats. They chant a chant to chant away Bartholomew's hat. According to them, "'Our charm will work in ten short years'" (100), and the impatient King kicks them out of his throne room. In their defense, it might have worked, but now the world may never know.
For our purposes, this guy's more bowman than yeoman. Looking dapper all decked out in Lincoln green, he tries to shoot off Bartholomew's hat with a bow "as big as a tree branch" and arrows "twice as long as Bartholomew, and thicker than his wrist" (86). It works about as well as you'd expect.
Despite his 9 to 5, the executioner is described as a "very pleasant man" (108). Hey, it's tough out there; guy's got to make a living. Although ordered to execute Bartholomew, he can't, because the rules state you can't execute someone with his hat on. He flicks a few of Bartholomew's hats off, mutters a "'Fiddlesticks,'" and promptly sends the kid out of the dungeon (118).