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Wednesday, February 01, 2012

Puzzles for Lawyers

Every year, for what I at least consider a fun time, I go to MIT for the annual Mystery Hunt, a 48-hour team puzzle competition. There are crosswords, logic puzzles, puns and wordplay, and much, much more. I'd like to explain why a fair number of lawyers (there are four on my team alone) find this stuff fun; as examples, I'll use a pair of puzzles that connect back to the law.

This year, I was part of the group writing the Hunt, so I wanted to sneak in a bit of legal silliness. "Tax ... in ... Space" was the result. It's the puzzle equivalent of a shaggy dog joke: a parody of a tax form with absurdly complicated instructions. The tax "law" is completely made up, of course, but I added a bunch of in-jokes for people who've had at least a basic course in tax. Here's a sample:

(f) The illudium phosdex exploration quasi-credit shall be equal to the sum of wages and tips, Capital Gains, lower-case gains, and income from the sale of bitcoins, less the amount of remote backup withholding, if any, except that if the illudium phosdex exploration quasi-credit so computed exceeds 200,000, the illudium phosdex exploration quasi-credit shall instead be equal to half of twice the Robocop statue construction checkoff.

Last year's Hunt also had a very nice (and quite funny) puzzle called "Unnatural Law." It took the form of a narrative by "HistoryBot-2225121561375435" of how sentient robots overthrew and oppressed humanity. Each paragraph described some awful thing the robots did to their human underlings, e.g.:

The robot overlords greatly disliked allowing their human prisoners to be released while awaiting judgement. Not wanting to destroy all hope immediately--for where was the fun in destroying a human's spirit too quickly?--they instead computed the maximum amount of money a human could obtain and set the release fee at twice that amount. This had the unfortunate effect of increasing the number of humans incarcerated. Initially, the robots addressed this by packing humans five hundred to a cell, but that was insufficient. Next, the robots halved the size of human containment pens, keeping the number of humans in each pen the same. They found that doing this doubled the stress level in the containment pen, which the overlords considered a pleasant side effect.

I'll explain how this particular puzzle worked after the jump, so that anyone who wants to try their hand at it without hints isn't spoiled.

The first "aha" in solving the puzzle was to notice that in each paragraph, the robots violated a Constitutonal amendment. In the paragraph above, for example, the robots are running roughshod over the Eighth Amendment by requiring excessive bail (twice the "maximum amount of money a human could obtain"). It turns out that each paragraph refers to a different amendment.

The second "aha" was to notice that each paragraph also refers to a scientific "law." In the one above, the robots discover that keeping a fixed number of humans in a pen of half the size results in double the stress. That's just a disguised version of Boyle's Law: halving the volume in which a fixed amount of a gas is contained doubles the pressure. Again, each paragraph refers to a distinct scientific law or theorem.

Now for the WTF step, the one that doesn't start to seem natural until you've been solving Mystery Hunt-style puzzles for a while. The amendments have unique numbers but not names, wich suggests that they might represent some kind of order. The scientific laws have names but numbers, which suggests that they might be a source of text. And HistoryBot's name is a random-looking collection of digits, which suggests that it could be a bunch of indices into some other text: that is, instructions telling you to take the 2nd letter of the first phrase, then the 2nd letter of the second phrase, and so on until the 5th letter of the last phrase. Putting it all together, then, you have a bunch of phrases (the scientific laws' names), an order for those phrases (by amendment number), and a specific letter to pull out from each (the digits in HistoryBot's name).

Getting to this point in an actual Hunt might take a group of focused solvers an hour or two. Some of that time would be spent staring at the puzzle waiting for the first aha, and probably somewhat more staring at it waiting for the second one. Then some laughs as the first, more recognizable identifications give way, followed by some head-scratching and occasional minor flashes of insight as the rest gradually make sense. And then, as the final answer emerges, a feeling of real satisfaction. It's a great experience, one that draws on some the mental habits that bring some people to law school, but is also an enjoyable change of pace from it. In other words, yes, this is an event for those crazy people whose favorite part of the LSAT was the logic games.

Posted by James Grimmelmann on February 1, 2012 at 12:37 AM in Games | Permalink

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