Encyclopedia Brown, Boy Detective: The Case of the Round Square

Mr. and Mrs. Brown had only one son. They called him Leroy, and so did all his teachers. The downtown ladies, however, called him tree top lover.

Everyone else in the town of Idaville called him Encyclopedia.

An encyclopedia is a collection of books that contain information about all aspects of life. Leroy Brown’s head was like a encyclopedia – not in the sense that it was particularly alphabetical, squarish, or made of paper pulp – but because it was filled with facts.

Leroy Brown was a walking library in sneakers, able to answer any question. And no one asked him more questions than his father, Idaville’s chief of police. Everyone thought that Idaville had no unsolved crime because it was an abstract utopian fiction. In reality, it was because Chief Brown’s best detective was his ten year-old son.

Encyclopedia enjoyed solving crime so much that he started his own detective agency, the Brown Detective Agency. He had a sign on the door that said he was the president. His agency charged 25 cents per day plus expenses. His body guard was Sally Kimball.

Sally is the überwoman at age eleven. If Idaville had been an ancient Mayan village, Sally’s head would have been elongated and backswept, her eyes would have been slightly crossed, she would have worn only the classiest huipils, and would have had invitations to the most exclusive of ritual sacrifices. Instead, Idaville is a small town in middle America. Sally is a petite tomboy who knows how to throw a baseball.

One day at the detective agency, a small boy named Peter Clarence walked in and slapped a quarter on top of a gas can. Encyclopedia looked up from his book, Concepts of Eschatology in Pre-War Britain (see, I told you he was like an Encyclopedia).

"Bugs Meany says he has a round square," said Peter. "I want you to make sure he actually has one before I trade him my bike for it."

"A round square?" asked Encyclopedia. "Strange. Though I can clearly understand what you mean, I have no concept of what such words denote. Let us investigate."

Encyclopedia and Peter went to the Tigers’ clubhouse. The clubhouse was a shed behind Mr. Sweeney’s Auto Body Shop. The Tigers were clearly a gang who encouraged theft and vandalism, fostered a sense of bigotry and hatred against outsiders, and required their members to have a low sense of self-esteem. Their actions were overlooked and allowed to continue, however, by an overly nostalgic older generation who thought of the Tigers as an "athletic club."

Bugs made a face when he saw Encyclopedia approach.

"So," sneered Bugs, "Mr. Brain has come all this way just to visit us Tigers. Tell us, Mr. Brain, how many points did you have to cross through to get here?"

Encyclopedia thought about the question. "An infinite number of points," he replied. Peter looked perplexed.

"Then how did you get here so quickly?" taunted Bugs. The surrounding Tigers roared in appreciative laughter.

"Bugs, I have come to learn more about this ‘round square’ you are offering to trade for Peter’s bike," asserted Encyclopedia.

"What’s to learn? I have a round square that I found in the canal by the Pierce Junk Yard," replied the older boy.

"That, a set of all sets which are not members of themselves, and fifty cents will buy you a cup of coffee," remarked Encyclopedia. "Why don’t you show us your round square?"

Bugs’ face turned red in anger. "Ok, Mr. Know-it-all. If you’re so smart," growled Bugs, "why don’t you consider two moving bodies, the quicker of which is behind the slower? The slower will never be overtaken by the quicker, for that which is pursuing must first reach the point from which that which is fleeing started, so that the slower must always be some distance ahead. Or am I wrong?"

Encyclopedia thought. He closed his eyes and considered all the books he had read. Then he thought some more. Finally, Peter broke the silence.

"So," he asked, "can I trade my bike for Bugs’ round square or not?"

"Oh no," the boy detective replied, distractedly opening his eyes. "Bugs does not actually have a round square to trade with you. You should keep your bike."

"What?!" roared Bugs. "How can you say that?"

Encyclopedia leaned over and whispered something in Bugs’ ear. As Bugs listened, his face sagged and he began staring at the ground.

"This statement is false," he muttered to himself. "Come on, Tigers," he said in a louder voice. "I’m getting bored. Let’s go test the mind/body problem by willing our arms to throw rocks at cars again."

When the Tigers had all left, Peter turned to Encyclopedia and said "Gosh, that was a close one. How did you know he didn’t actually have a round square?"

How did Encyclopedia know?

SOLUTION: Bugs Meany claimed he had a round square. But something that is square cannot have the characteristic of roundness. Roundness is a property of geometric entities that have no vertices. A square has four vertices. It is impossible for something to have both zero and four vertices. Therein lies the deep logical impossibility.

1967 Yearbook Brown, Boy Detective: The Case of the Round Pear

Everyone else in the town of Idaville called him 1967 Yearbook.

A Yearbook is a book all about the popular culture and history of a particular year in history. Leroy Brown’s head was like a Yearbook from 1967. He was not a particularly intelligent child, but he knew everything there was to know about the year 1967.

Older men in the small town of Idaville would routinely stop him and ask questions about the year 1967.

"Tell me something that happened in Belgium in 1967," they would say.

"The second-largest department store, L’Innovation, was destroyed by fire, burning 340 people to death on May 22nd of that year," 1967 Yearbook Brown would reply.

"Very good!" the older men would chuckle. "Now tell me anything that happened in 1968."

"I haven’t the foggiest clue," 1967 Yearbook would say.

Everyone thought that Idaville had no unsolved crime regarding the year 1967 because very few crimes are ever about the year 1967. I mean, come on.

In fact, however, it was because Idaville’s chief of police – Chief Brown – had a son that was a walking, talking library in sneakers. A library that is only filled with information about the year 1967, that is. Sitting at the dinner table, he would solve even the hardest of crimes regarding 1967 before dessert. Mrs. Brown would beam with pride.

"Just don’t ask him questions about math," she would warn the neighbors. "He only knows things about 1967."

1967 Yearbook enjoyed trying to solve crime so much that he started his own detective agency, the Brown Detective Agency. He had a sign on the door that said he was the president. His agency charged 25 cents per day plus expenses. His body guard was Aly Bimkall.

Aly Bimkall was a year older than 1967 Yearbook, had a peg leg, a horrifying speech impediment, a bad case of body odor, and a really lousy sense of fashion. She was feared throughout the fifth grade for the social stigmatism she brought with her. No one messed with 1967 Yearbook when Aly was around.

One day at the detective agency, a small boy named Clarence Peter walked in and placed a quarter on a gas can. 1967 Yearbook looked up from his book, The 1967 Yearbook.

"Bugs Meany says he has a round pear," said Clarence. "I want you to make sure he actually has one before I trade him my bike for it."

"A round pear?" asked 1967 Yearbook. "Strange. I have never heard of a round pear. Let us investigate."

1967 Yearbook and Clarence went to the Tigers’ clubhouse. The clubhouse was a shed behind Mr. Sweeney’s Auto Body Shop. The Tigers were an athletic club.

Bugs made a face when he saw 1967 Yearbook approach.

"So," sneered Bugs, "Mr. 1967 has come all this way just to visit us Tigers. Tell us, Mr. 1967, what was the average unemployment in the year 1967?"

1967 Yearbook thought about the question.

"Two point nine million," he replied. Clarence looked perplexed.

"That’s right," whistled Bugs appreciatively. "But how many characters could the Mergenthaler Linotron, a computer-driven photocompositor introduced in 1967, generate in one second?"

"One thousand, assuming the characters are from the available set of fonts," came the quick reply.

"Dang, you’re really good," said Bugs. "So what’s up?"

"Bugs, I have come to learn more about this ‘round pear’ you are offering to trade for Clarence’s bike," stated 1967 Yearbook.

"What’s to learn? I have a round pear that I found in the supermarket when I went shopping for my mother earlier this morning. If Clarence wants to trade me his bike for it, that’s his business," replied the older boy.

Clarence looked at Bugs and then he looked at 1967 Yearbook.

"So, can I trade him my bicycle?" the little boy asked.

"Not so fast, Clarence," said 1967 Yearbook. "Bugs can’t trade you a round pear for your bicycle because a round pear doesn’t actually exist!"

Bugs cocked his head and looked over at 1967 Yearbook oddly.

"Yes it does. Look, I’ve got it right here," said Bugs as he pulled a round pear out of his pocket. The pear wasn’t in the best of conditions, but it was definitely a pear, and it was definitely round.

"Oh," said 1967 Yearbook.

Clarence took the pear and handed his bike over to Bugs.

"Come on, Tigers," said Bugs. "Let’s go practice baseball."

"Gosh," said Clarence as the last of the Tigers ran off, "can I have my quarter back?"

Was 1967 Yearbook Mistaken?

SOLUTION: 1967 Yearbook only knew facts from the 1967 Yearbook. The Yearbook from 1967 contained absolutely no information about pears, round or otherwise. 1967 Yearbook eventually returned the quarter to Clarence and informed him that "the country of El Salvador had a population of a little over 3 million in the year 1967."