This is an explanation of the third logic game from Section II of LSAT Preptest 74, the December 2014 LSAT. Game three involves the following setup:
There are six colors of thread: forest, olive, peach, turquoise, white, and yellow (F, O, P, T, W, Y). Five out of six colors of thread will be use to create three woven rugs. The rugs are either made from a single color or several colors. The rules allow you to determine the possible color composition of the three rugs.
This is a tricky game to explain. It’s not necessarily a hard game to do. That’s because this game depends on your ability to see how the rules combine. There are almost no upfront deductions, and not even a good general template you can make. So my explanations for this are limited because I can’t go inside your mind to show you how to see the game.
This game is a test of your visualization abilities. I am firmly convinced that how you lay diagrams out on your page significantly affects how well and fast you can do games. I do two things:
- My main diagram is on the second page, just under the questions.
- I make new diagrams for each question that requires it.
This significantly reduces eye tracking time. If your diagram is right beside answers, there is no delay between seeing the diagram and judging whether an answer is possible.
Having the main diagram on the second page also helps you reference it faster. I don’t draw anything else in the main diagram area. Having a page free of clutter reduces how hard your brain has to work at understanding the diagram.
There’s one more trick: make things explicit.
For instance, suppose a question places O and P. It’s helpful to then draw a list of who’s left beside the diagram: F, W, T, Y.
Drawing F, W, T, Y seems obvious, and therefore useless. But having the remaining variables visible lets you mentally move them onto the diagram. This removes the need to draw multiple diagrams to test the slight changes.
Ok, enough preamble. Lets see how to draw these rules. I’ll note that there are rules in the setup paragraph too:
- Exactly 5/6 rug colors are used.
- Rug colors aren’t repeated.
The first one is most important. If one color is out, that means all the other colors are in.
Note also that no rug can have more than three colors. The possible color distributions among rugs are as follows:
Those are the only ways to have three rugs that have a total of five colors.
Ok, the first rule: if white is used, then two other colors are used.
Note that this forces the game into a 3-1-1 color distribution.
Next, if orange is in, then it goes with peach. This leads to a deduction I’ll discuss later:
Rules 3, 4 and 5 say who can’t go together:
This last rule isn’t worth completely memorizing. Instead, have a clear drawing that you can reference in a split-second. Though I did remember that both peach and turquoise were mentioned in two of the exclusion rules.
I mentioned there was a deduction. Deductions come from looking at all of the rules and thinking about how they interact. Deductions also come from past experience on other games. If you know past games well enough, you’ll see similar deductions on new games.
We need five colors. If any one color is out, then all the others are in.
This has a big effect on peach. If orange is out, then peach is in (because all other colors are in). And if orange is in, then peach is in (rule 2).
So either way, peach is always in. This solves question 12 instantly. Surprisingly, this deduction wasn’t useful on any of the other questions.
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