Logic Game Algorithms

Cant Get Right

So I was watching a thing on Netflix about algorithms and, all of a sudden, the guy starts explaining what I think I recognize as the weird game from PT 77. I checked it out, and sure enough: It’s a really simplified version of the Gale-Shapley algorithm which won a Nobel Prize in 2012. I don’t know anything about algorithms, but I wonder if there are other well known algorithms that could appear in the games. I think some basic, common algorithms would make for a really interesting and potentially somewhat relevant study. Certainly a familiarity with the Gale-Shapley algorithm would have made 77 G3 a breeze. It’s probably a bit far reaching to include in LSAT study proper, but I think it would be an interesting side project that could develop some relevant skills and teach exactly the kind of abstract thinking which is so important on Games and especially when weird games pop up.

So anybody know any cool algorithms they think would be worth checking out?

BruiserWoods

(haven't don't pt 77 yet - but) ahhhhhh what??? *hides under rock*

Cant Get Right

Haha @BruiserWoods. What, you don't study math recreationally in your down time?

BruiserWoods

@"Cant Get Right" i did read a book on Fermat's Enigma once. But it was more of a biography. And I didn't understand a lot of the maths

quinnxzhang

If you're looking for some algorithms that will train your logical reasoning, then I think any of the standard sorting algorithms (insert sort, merge sort, bubble sort, etc.) would make good material. You could also look into some of the more sophisticated graph search algorithms (A*, backtracking, Dijkstra, etc.). Reading the descriptions, learning how they work, and understanding why they belong to the complexity classes they do involve a lot of the same kind of precise, rule-driven thinking that goes into doing LGs.

I also think doing some of the tech-interview puzzles/brainteasers would make for good mental exercise. Some of the better known examples include the blue-eyes problem, the five pirates problem, the double egg drop problem, the wolf-sheep-cabbage problem, etc.

For a really sad drinking game, you and your friends could try your hands at constructing some busy-beaver algorithms and seeing who wins (I distinctly remember agonizing over this in my computability course). In case you're ever interested, this problem also segues nicely into some fascinating theoretical results around the halting problem and incompleteness theorems!

I do want to say that studying algorithms for practice and for mental exercise is one thing, but thinking they'll directly help on the LSAT is another (not that I'm accusing you of saying this). For example, checking whether a game board is possible is really just a glorified Boolean satisfiability problem (SAT). But SAT is an NP problem, so even the best SAT algorithms would probably take longer than the entire LG section to work through! Even though it would take a computer a long time to check whether a game board is possible, presumably you can do it much faster by using some simple heuristics and having a high-level conceptual understanding of the rules, and I think training these latter skills is much more important for LGs than knowing algorithms is.

apublicdisplay

@ Cant Get Right, that actually sounds really interesting. What was the name of the show?

Cant Get Right

@apublicdisplay "The Secret Rules of Modern Living: Algorithms"

Cant Get Right

Thanks for the suggestions @quinnxzhang , I’ll check those out!

Cant Get Right

@BruiserWoods have you heard of the Millennium Problems?
claymath.org/millennium-problems
$1,000,000 to anyone who can solve one. I don’t know much math, but if you’ve got any interest in things like Fermat’s last theorem, they can be fun to read about.

quinnxzhang

@"Cant Get Right" said:
$1,000,000 to anyone who can solve one. I don’t know much math, but if you’ve got any interest in things like Fermat’s last theorem, they can be fun to read about.

Reading about the drama around these things is a guilty pleasure of mine. Perelman (https://en.wikipedia.org/wiki/Grigori_Perelman) solved the Poincare conjecture, one of the Millennium Problems, but made it a point to decline both the Fields Medal and the Millennium Prize. Even more, the New Yorker published a very controversial article (https://en.wikipedia.org/wiki/Manifold_Destiny) about the human side of this problem, which probably contributed to Perelman's eventual withdrawal from mathematics!

Cant Get Right

Yeah @quinnxzhang all this stuff is really fascinating. Man, if I were living in an apartment with my mom, it’d be tough to turn down all that prize money!

Cant Get Right

Just came across another logic game out in the real world and figured I'd share. About 15 pages from the end of "HP & The Sorcerer's Stone," they've got to solve a sequencing game to know which potion to drink so they won't burn to death. I stopped and worked out the rules. Nothing too complicated, but fun to be able to apply LG skills in a real life situation. That's right, I said real life. Magic is real. We've known about it for some time now.

It's a big offset block of italics right towards the very end for anyone who wants to look it up. I'd post it, but I'm sure the licensing fees on that would be slightly higher than whatever LSAC charges!