Linear Setup Practice Drill #5

[btownsquee]

Hello,

When doing problems like #5, I end up writing out the different possibilities of the order of the performances. Based on that order, I see trends like the fact that neither Q or R end up at the 2nd and 6th blocks. I used this to figure out the answer to Question 5.1. Is there a better strategy to use in order to solve problems like this?

Thank you very much!

[Adam Tyson]

Hey there, btownsquee, glad you asked about that, because you've described what I think is a pretty common approach taken by a lot of students on a lot of games that, while it may produce useful results, is usually a real time suck that isn't worth it. Let's look at the setup for that scenario and see what we can infer without doing all those possibilities.

(Now you'll have to forgive me in advance for how ugly this is about to look)

Our base is 7 slots numbered 1 through 7, and we can place S in the 4th slot per the 3rd rule:

__ __ __ S __ __ __
1 2 3 4 5 6 7

The 1st and 4th rules give us an FG block, while the 2nd and 5th rules give us an HJ block. What will we be doing with those two blocks? We'll need to place one of them before S and one after S. There's no way to tell which goes where, as we have no more sequencing rules to guide us. In fact, no more rules at all! What we have left is just two variables, Q and R, that haven't been mentioned in the rules. Those are our "random" variables.

Now, without drawing a single solution or template, what can we visualize here? One of those two blocks goes before S leaving room for just one more variable in those first three slots. That one additional variable has to be Q or R, a random. The other of those blocks goes somewhere after S, partnered up with the other random, Q or R. No need to write any of that down - it's pretty clear to the naked eye already, right?

At this point, you could make a couple useful inferences, the same ones you figured out doing things the long way: neither Q nor R can be 2nd or 6th, because placing either of them in either of those spaces will break up one of those two blocks. That's great, and if you like not-laws as much as I do (not everyone does), you add those not-laws to your diagram. Because I like them so much, I also added not-laws under space 3 for F and H and under 5th for G and J. I could have also added F and H not-laws at space 7 and G and J not-laws at 1, but it started to feel like overkill to me, and the blocks told me enough about that to make me feel comfy without doing so, so I just moved on without them. It's your call as to whether you do more, less, or the same number of not-laws as I did, but I would be willing to bet at least one question is going to test the inference about Q and R in those spaces, so I would have them for sure.

I haven't drawn a single solution, not even a template at this point, but I can answer question 5.1. It's all about what can be next to what, and I know a lot of things that cannot be next to each other. F and J, for example, cannot be next to each other because they are in blocks that are separated by S. All the answer choices mention Q or R or both, and I know for sure, again because of the split around S, that those two can't be next to each other, although either of them can be next to any other variable. A quick scan through the answer choices should be all you need to see that E won't work, because you have already prephrased it by now. However, if I want to be more meticulous I look at answer A and imagine (not write down, just visualize) an order of RFG, which works either at 1-2-3 or at 5-6-7. I scan the other answers and can imagine all but the last one working. Boom! Either way, the question is answered in, I expect, much less time.

Once you have the basic structure down and have a good grasp of the game, drawing out solutions is typically going to waste time. There are a rare few games where that is the best approach, and typically you will recognize when that is the case because you will have virtually nothing else to go on and your diagram of the rules will look as empty as a ghost town. Here, though, where so much is clear from the setup, I suggest just jumping into the questions and applying what you know. You may end up doing some specific solutions for some of the questions, but many will test your more general understanding of how the game works in a big-picture sense. That's what this question is doing, and no specific mini-diagram should be required.

Give that approach some thought and see if you can save yourself some time on other games by pausing and reflecting on the diagram briefly before going to the questions. See if any big inferences come up, and if you have a good sense, without details, of how things are going to go. That big-picture view will serve you well time and time again, so develop it through practice.

Good luck, keep pounding!

[btownsquee]

Thank you very much! This helps a lot.