“Evidence?”
There must be a mistake. They must be confusing me with another faculty member. Yes, that must be it . . . a mix-up.
With that soothing thought in his mind, Albert gingerly opened the solid oak door to his office.
In front of his desk in one of the tiny chairs that his students usually occupied during office hours sat the massive frame of a policeman. The sight of this mammoth man squeezed into a chair meant for a considerably smaller individual would have been comical had it not been for the circumstances. Albert wondered how it was that a single man could so drastically shrink his previously roomy office.
The policeman extricated himself from his entirely inadequate seating, extended his gigantic hand, and gave Albert a warm smile.
“You must be Professor Puddles,” said the detective. “I’m Detective Michael Weatherspoon, Princeton Police Department. It’s a real pleasure to meet you.”
Albert felt like a child in the presence of the bearish detective and meekly shook his hand.
Weatherspoon resumed his seat, inviting Albert and Ying to join him. “I’m sorry to bother you, Professor, but there was a burglary last night.”
“Oh, I’m sorry to hear that, Detective. Where?”
“At the Bank of Princeton,” chirped Ying, sliding forward in her chair.
“That’s right, little lady,” said the bemused detective, running his hands through the gray remains of what looked to have once been a world-class Afro.
Ying attempted to stifle her mischievous grin. “Sorry, I just feel like I’m in an episode of Law and Order.”
Detective Weatherspoon chuckled and shook his head.
“Sorry, Detective. Please continue,” said Albert.
“The security guard on duty was killed attempting to stop the thief.” The detective carefully removed a picture from his file and handed it to Albert. He recoiled as he saw the prostrate body of Wally McCutcheon on the floor. Wally was a gentle-looking older man, and Albert couldn’t help thinking of his grandfather.
“Who would do something like this?” asked Albert, suppressing an unwelcome spasm of emotion.
“We don’t have any leads yet, but we do know from the security feed that, before he died, the security guard was able to rip a sliver of paper from the assailant’s coat pocket.”
The detective removed a copy of the paper and placed it on Albert’s perfectly ordered desk.
“At first, we thought it was a scientific formula, so we took it down to the chemistry department, but they said that it was some kind of game tree and that you’d be the man to talk to. What do you make of it?”
Albert studied the piece of paper, attempting to ignore Ying’s curious glances over his shoulder.
“Well, this is clearly an issue tree or game tree. Mathematicians, logicians, and computer scientists use these in rudimentary problem-solving, computation, and decision analysis to ensure that their thinking is perfectly logical or ‘MECE.’”
“I’m sorry, MECE?” asked the detective.
“Yes, mutually exclusive and collectively exhaustive. To properly consider any problem, it’s critical to weigh all of the options. For example, say your in-laws are in town.”
The detective rolled his eyes at the thought.
“You would want to logically assess what hotel you should have them stay at so that you’d be confident you weren’t overlooking a good option. That’s the collectively exhaustive part. Then, once you had your list of hotels, you’d want to make sure that it didn’t overlap in any way.”
Weatherspoon’s furrowed brow conveyed a combination of confusion and irritation.
Albert pressed on. “For example, if you initially broke down hotels into two categories—hotels with rooms and hotels with parking—that would be collectively exhaustive because all hotels have rooms, right?”
Detective Weatherspoon nodded.
“But it wouldn’t be mutually exclusive because there are some hotels that have both rooms and parking, so they would sit in both categories and muddle your thinking. To be fully logical, you would have to start with a different categorization of hotels that was completely MECE, such as hotels within Princeton city limits and hotels outside Princeton city limits. Every hotel on earth would fit into these categories, so it would be collectively exhaustive, but none would overlap because they are either in Princeton city limits or they’re not, so it’s mutually exclusive. Once you’ve settled on those base categories, you then add additional branches to the tree until you’ve settled on your answer.”
Albert walked to the small chalkboard next to his desk and sketched a game tree depicting the hotel decision-making process:
“It’s quite fun, isn’t it?” Albert said with a twinkle in his eyes.
The detective coughed. “I don’t know about fun, but it’s certainly enlightening, and it will help the next time the in-laws are in town. So, what does this game tree mean?” he asked, pointing to the scrap of paper. “I’m assuming it’s not about where the criminal will be vacationing?”
Albert had been so caught up in the joyful world of game trees that he’d forgotten all about the task at hand. Resuming his serious posture, Albert returned his gaze to the game tree before him.
The tree in question was rudimentary but, due to the use of random letters rather than words within each box, extremely difficult to understand. In addition, the use of the words “prima facie” at the top of the page implied a multi-scenario analysis of which he had one page.
Albert shrugged. “Honestly, Detective, at first glance, I can’t tell you much. Judging by the size of the tree, the analysis is relatively basic, but because it is just the base case, there could be more to the analysis. The shaded boxes show the path of decisions made by the tree’s maker. Until I know what the letters symbolize, I can’t possibly tell you what the tree means. The letters almost certainly represent some type of cipher or code, but I can’t be sure until I look at it in more depth. Give me some time and maybe I can identify a pattern.”
“OK, Dr. Puddles, I’ve got to go home and feed the
