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AL – So there’s a far-off place that consisted of a perfectly triangular lake surrounded by land, with three kingdoms, one on each side of the lake. The first kingdom is rich and powerful, filled with wealthy, prosperous people. The second kingdom is more humble, but has its fair share of wealth and power too. The third kingdom is struggling and poor, and barely has an army.
The kingdoms eventually go to war over control of the lake, as it’s a valuable resource to have. The first kingdom sends 100 of their finest knights, clad in their best armor, and each with their own personal squire. The second kingdom sends 50 of their knights, with fine leather armor and a few dozen squires of their own. The third kingdom sends their one and only knights, an elderly warrior who has long since passed his primes, with his own personal squire.
The knight before the big battle, the knights in the first kingdom drink and make merry, partying into the late hours of the night. The knights in the second kingdom aren’t as well off, but have their own supply of grog and also drink late into the night.
In the third camp, the faithful squire gets a rope and slings it over the branch of a tall tree, making a noose, and hangs a pot from it. He fills the pot with stew and has a humble dinner with the old knight.
The next morning, the knights in the first two kingdoms are hung over and unable to fight, while the knight in the third kingdom is old and weary, unable to get up. In place of the knights, the squires from all three kingdoms go and fight. The battle lasts ling into the night, but by the time the dust settled, only one squire was left standing—the squire from the third kingdom.
And it just goes to show you that the squire of the high pot and noose is equal to the sum of the squires of the other two sides.

Context

I like to collect jokes, specifically puns, on various topics so that no matter what situation I am currently in, I can say, “Oh, I know a joke about that!” I have found that most people have a love/hate relationship with puns; they tend to love telling them and hate hearing them. I mostly tell puns to family and friends, and their anger and frustration fuels me. Though my friends groan and sigh every time they hear a pun, they will still send me any good ones that they find. I also find puns on various social media platforms, in books, and on the occasional popsicle stick. Any time that I find or am sent a pun that I like, I write it in a book that I keep specifically for this purpose. My very favorite kinds of puns are the ones that are long and drawn out, ones that are a paragraph, maybe two, and you get to the end and the last line is a clever pun that uses many elements of the story that came before it. My second favorite kinds of puns are the short rude/dirty ones, because in addition to the reaction you get for any other pun, you also get the shock reaction from the vulgarity. I save the more risqué puns for close friends, as I don’t want to offend the delicate sensibilities of people that I don’t know very well.

Analysis

This pun begins as a lengthy narrative that misleads the listener from thinking about puns. The punchline is succinct. And it is not necessarily comprehensible to everyone. Specifically, the listener must have a basic understanding about geometry. What initially sounds like an attractive David-and-Goliath story is actually… a math joke. The punchline, “the squire of the high pot and noose is equal to the sum of the squires of the other two sides,” can be misheard (with the right mindset and maths knowledge) as “the square of the hypotenuse is equal to the sum of the squares of the other two sides.” Not only is the listener tricked into listening into a pun (as the informant mentioned, most people hate hearing them), but they are also tricked into having to think about math, which, depending on the audience’s preference for school subjects, is insult to injury.