Sunday, December 14, 2014

Logical Self-Congratulation

Hey! My solution to the "extremely difficult" Star Trek puzzle I posted last week is reprinted today at io9 with my permission (scroll way down).

I worked the puzzle out while watching my students take a final exam. I was interested in it mainly because I teach a course on discrete math, covering things like formal logic, relations, and graph theory, and I'm always looking for interesting new problems. But as a mathemagician, I'm more interested in how to create puzzles like this than in how to solve them. I wonder how Professor Finkel did it? Perhaps he added one statement at a time until his program gave him a single solution. From a logical point of view, it was much simpler than it need have been, given that only one statement connected the two "parts" of the puzzle.

Robbie Gonzalez, the column's author, says this about the puzzle:
I'm going to come right out and say it: This puzzle is, in fact, "extremely difficult." It is not so much one puzzle as it is several logic puzzles. Some of those puzzles are nested, such that certain conclusions cannot be made until one has accurately arrived at some other conclusion or conclusions. This kind of puzzle can get very complicated very quickly, and solving it typically involves the use of a spreadsheet or some kind of table to keep track of all the relationships in play. 
It's also the kind of puzzle that begs for a programmatic approach. And, in fact, that's exactly how Finkel [the professor who created the puzzle] solves it himself. "This admission may come as a surprise," he writes me by email, "but I have no idea how to attack this puzzle with pen and paper!"
Well, now he and the rest of the Internet know. And maybe, because of that knowledge, the world is just a tiny bit less dark, a tiny bit less confusing. Maybe someone, somewhere, will go to sleep easier tonight, knowing which Enterprise NCC-1701-D crew member outranks which at Fizzbin. Just maybe. And that makes it all worthwhile.


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