Game #4 - Four Employees Transfer Workpieces

[GeneW]

Can someone please post a diagram for this game? Thank you in advance.

[elanaminkoff]

yes. i too am really struggling with this. I have managed to work out that it should essentially be a grid with four rows and four columns.
I set it up with days of the week as my base and then each work piece would be transferred horizontally, and since there were four work pieces i built up 4 rows above each day of the week.
I am struggling with inferences though. I know that the first day is arbitrary and you can just list out m,j,k,l. and then since k and l both can't transfer to j and j can't transfer to itself, m must go to j. after that i can't seem to come up with much, and i found myself relying on brute force for most of the answers which is VERY time consuming on!
Please help with ways to speed this up!

[christine.defenbaugh]

Thanks for asking elanaminkoff and GeneW!

Man, Summit Company has been the talk of the TOWN since June. This is just one more example of the LSAT demanding that we move beyond just being able to regurgitate familiar game families and their optimal automatic diagrams.

We've actually put together an entire video explanation of the game and all the questions for you guys! Check it out!

CLICK HERE for the Super Fabulous Manhattan LSAT Video Explanation for PT72, G4!

Now, for those of you that can't watch the entire video right now (hmmmm, browsing the forums from work, are we?), diagramming this game is tough. I'll be perfectly honest - when I did this game the first time I jotted down a diagram at the beginning of the game that I never used at all. I abandoned it and rediagrammed a few things partway through the questions. However, at no point did this game ever have a truly robust diagram in the way that most games do. This is actually a fairly common irritation for games like this - we call them Transposition games.* There is no fixed, standard optimal diagram. Instead, we have to pick from the various tools in our toolbox of diagramming awesomeness and cobble something brand new together that reflects what's happening in the game.


*If you want to take a look at some other games that fall into the category of Transposition, here's a list:

PT10, G3
PT11, G4
PT12, G4
PT13, G4
PT16, G4
PT18, G4
Feb97, G3

We know we have four (named) employees (J, K, L, M), four (unnamed) workpieces, and four days of the week. Since we know that each person works on exactly one workpiece a day, we could start out with grid, as elanaminkoff did:

This is a perfectly reasonable way to think about this game. Next stop - notice that you only have three rules about people who can't transfer to each other:

These rules are way more useful though, when we turn the negatives into positives. If J cannot pass his work to M, nor back to himself, the only options left are that he passes to K or he passes to L.


The game changer is making the next inference. Since everyone has to work, and K won't give work to J, and L won't give work to J, and J can't give work to himself..... that means M is forced to give work to J, every transfer. If M did not, J wouldn't get work from anyone at all.


Now armed with this information, we can charge back to our grid diagram!

Unfortunately, there's just not a ton that we can actually fill in right now. There are way too many possibilities. At this point, there are a number of perfectly legitimate paths to take.

1) go ahead and dive into the questions and fill in hypo grids as you go
2) diagram what could happen to any given workpiece
3) diagram what could happen on any given day

For #2, we simply need to start combining the rules we already have about legal transfers. With our M->J inference, we have a complete listing of all valid moves. Put them all together, and you get this:


Remember, this is not a diagram that shows the actual transfers that MUST occur, but rather one that shows the options at any given point. If a workpiece started with K, it might have a journey of K-M-J-L, or perhaps K-L-K-M! Or a number of things!

Now, this is a bit different than considering what might happen on any given day. If we went down this road (#3 above), then we'd want to keep in mind that on any given day, every person has to work. So, on any given day, we know that M always passes to J. J has to also pass his work off to someone, and there are only two options for who that can be: K or L.

Once J passes off to K, though, K doesn't have as much flexibility as you might think. If K were to pass to M, then L would be screwed over in the exchange! No one would pass to him and no one would receive work from him. So, K doesn't have the option to pass to M, he must pass his work to L.

If J instead passes his work to L, L ends up in a similar predicament. So, there are actually only two loops possible for any given day (K and L just flip flop in the line up):

Once again, notice that there's no defined starting point - these are loops.

So, what's the optimal diagram: grid, flowchart for any workpiece, or loops for any day? It's debatable! The most important thing is to stay flexible. All three of these diagrams are useful, but you certainly don't need them all to have an adequate understanding of the game.


Please let me know if this above diagrams, or the video explanation were helpful!

[GeneW]

Thank you for the great video and written explanations, Christine. It's an unusual game.

[gaheexlee]

Hi Christine,

Thank you so much for your video and explanation!!

I did have one question though and was wondering if you could help? When solving #21, you crossed off (D) and (E) because you said M couldn't pass to anyone other than J. I understand how you got the M-J inference but what if the work day started with J and ended with M? This way, M doesn't have to pass to anyone. So the sequence for a particular workpiece could look be J-K-L-M or J-L-K-M; this doesn't violate any of the rules.

I have a feeling I'm just misunderstanding what you said about there not being starting points as everything is in a loop, but I didn't quite comprehend that part

[christine.defenbaugh]

Hey, gaheexlee, good question!

First, you've got to separate whether we're talking about what happens to a particular workpiece on M-T-W-R, or whether we're talking about all the transfers that happen (to all the workpieces) on the morning of one particular day.

Now, if we're looking at what happens to a single workpiece throughout the week, then you're 100% correct - J-K-L-M or J-L-K-M are completely legit lineups for the workers. If this happened, for this workpiece M would never pass to J. (Just remember that we're only looking at a single workpiece, though - the other three workpieces would have M passing to J somewhere in the lineup.)

But look carefully at what Question 21 is asking us: one workpiece is worked on by only two of the workers total for the entire week. So, in this situation, J-K-L-M and J-L-K-M aren't legal, because they have all FOUR workers working on the piece.

For (D) to work, for instance, the lineup for the workpiece would have to be either: K-M-K-M or M-K-M-K, since those are the only two workers allowed to work on it! In both of these scenarios, M ends up passing to K at some point, and that cannot happen! (Why can't it happen? On the day M passes this workpiece to K, J is sitting at some other table and no one will pass him work! M is *always* required to pass whatever workpiece he has that day to J, on every day that isn't Monday.)

The above diagrams are loops in that you can start ANYWHERE on the loop, then from that position look at what options you have available to you. (I.e., just because they both appear to "start" with M doesn't mean you have to start with M!). But it's absolutely critical to keep separate whether you're looking at what happens to a particular workpiece throughout the week, or whether you're looking for what transfers occur at the beginning of a particular day!

What do you think?

[gaheexlee]

Ah, you're a life saver. Everything makes sense now. Thank you so much for the in-depth reply and clarification!!

[hanhansummer]

Hello Christine,

I have a question on #23. I choose D because I think #21 illustrates a possibility for K-->L and L--K to work. And I am still confused why one workpiece can be worked by only two employees.

[emmahhz]

Hello Christine,

I have a question on #23. I choose D because I think #21 illustrates a possibility for K-->L and L--K to work. And I am still confused why one workpiece can be worked by only two employees.

Q23 asks which one could be true about TUESDAY. So all the works have been transferred ONLY ONCE. By "one work piece can be worked on by only two", it means FOUR-time transfers have been completed within ONLY TWO workers. So these two questions are targeting at different things.

For Q23, since we know that there are ONLY two possible transfer ways:

EITHER M-->J-->K-->L-->M OR M-->J-->L-->K-->M

One time transfer can use either way. And E conforms to the first one.