This is an explanation of the fourth logic game from Section III of LSAT Preptest 76, the October 2015 LSAT.
A publisher is planning to publish six cookbooks over the course of a year: K, L, M, N, O, and P over a course of a year. Each of them will be published in either fall or spring (F, S). You must determine the possible publishing schedules based on the rules.
Game Setup
Time on second attempt: 5:10 See “repeating games” at bottom of section for details.
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This is a grouping game, and a fairly simple one. You can make three scenarios upfront that determine everything. Normally, I don’t split games with more than two options, but I’ll make an exception for three-option games if they seem fairly restricted.
Here I initially planned to split the game on “M in the fall” and then “M in the spring”. But upon drawing those scenarios I saw that the “M in the spring” scenario split neatly into two, so I drew those. The point being, you don’t need to know in advance how many scenarios there will be: often there will be two major scenarios you can draw. Upon drawing them, it may become clear that one of those scenarios can be split further. At that point, you can do so if it makes sense. In this case it did.
(People ask: how do you know if it makes sense? Do it if the resulting scenarios are both very restricted and clear to read)
For this game (like all games), I read all the rules before I started drawing. That let me start with the most determinative rules: those that affect M. I saw M was in two rules, which means M has a big effect. So I first tried out the last rule: M in the fall.
That has two effects:
- N goes in the spring (rule 4)
- P goes in the spring (rule 1)
Next, look over the rules to see what else is affected. Rule two says that K and N must go together. So we must place K in the Spring:
Then check rule 3 to see if it applies. It doesn’t, since K isn’t in the fall. So this diagram is almost complete. We just have to figure out who hasn’t been placed. O and L are left. I draw them to the top right of the diagram, for a quick visual reminder of who needs to be placed. They can go in either fall or spring:
Note that I don’t draw a list of letters: K, L, M, N, O, P. What’s the point? In that format, they have no rules attached. You can’t do anything with them, it clutters up the page, and drawing them prevents you from thinking.
Scenarios with M in the Spring
So that scenario above is what happens if M is in the fall. For our other scenarios we’ll have to place M in the spring. If M is in the spring, P must go in the fall (rule 1):
We could just leave it there, and start the game. But K also has two rules attached to it. So we should try placing K, because we may end up with two very restricted scenarios. First lets place K in the fall. That means N must also be in the fall (rule 2):
Next, rule three says that if K is in the fall, so is O:
I also drew L above the diagram, to the right. L is a floating variable in this scenario: they’re the only cookbook left to place, and they can go in either season.
So that’s M in the spring, K in the fall. Finally, lets place M in the spring, and K in the spring:
Of course, since K is in the spring, then so is N (rule 2). O and L are floating variables that can go in either season.
That’s it: these three scenarios determine everything. To answer the questions, just check the relevant scenario.
I took a photo of my own drawings for this game, so you can see what it looked like on the page. I draw my main diagrams just below the questions, on the second page. That’s so I can easily locate them, without wasting precious working memory on eye tracking. Note that I also never touch that – drawing over them also scrambles your brain.
Photo of diagrams on page:
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Repeating Games
I’ve written elsewhere about the benefits of repeating games, to solidify your intuition for deductions. Note that the purpose of repeating games is to prove the answers right, so it doesn’t matter if you remember the right answer.
I repeated this game about three days after I first saw it, by which time I had forgotten the answers. I’ve written how long it took me on the second attempt. That time, or a couple minutes above it, is roughly the standard you should be aspiring to – a lot of people take 8-9 minutes on a repeat attempt, get everything right, and pat themselves on the back. But that’s too slow. The faster you go when repeating, the faster you’ll learn to go the first time you see a game.
(I say “a couple minutes above” my time because, after years of teaching the LSAT, I’m really, really fast. You should be almost as fast as me, but you don’t exactly need to match my pace to score -0.)
Time on second attempt: 5:10
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