LSAT 82, Game 3 Setup, Witnesses, LSATHacks

Game Setup

Time on first attempt: 11:40

This game is a mixture of linear and matching. You have to match prosecutors to witnesses, and place them in order. The witnesses are Farrell, Greer, Hong and Ikaba. They are interviewed over four days by three investigators: Qin, Rivera and Shaw.

Each witness is interviewed once, and each investigator will interview at least one witness. (One investigator will do two interviews)

For me, this was the hardest game of the section by far. I took 11:40 min to do it. I had time to do this because I had gone very fast on the easy games and had a buffer of time. If you ran out of time due to  this game, part of your training should involve redoing the easy games to get better and faster at those so you have that buffer too.

With matching games, I like to place the second variables under the diagram. In this case, investigators go below. Since rule 4 says R does the third interview, we can draw this on the diagram:

Next, you should think about what is the most restrictive element in the remaining three rules. (I failed to do this, and it’s what made the game hard for me.)

The restrictive element is this: the interaction of rules 1 and 3. Note these three things:

1. Rule 1: G and H must be interviewed by the same investigator.
2. Rule 3: Qin must interview F
3. Setup: There are only three investigators

We can conclude that one of the three investigators interviews twice, and the other investigators interview once. e.g. QRRS could be the four investigator.

The interaction I am talking about is this:

• Exactly one of the investigators interviews twice, and they interview G and H
• Therefore, it is not Qin who interviews twice, as Qin must interview F.
• Therefore, it is Rivera or Shaw who must interview twice, and they interview G and H.

So Q can only be placed once. And since R is in third, that means there are three places that Q can go. So we can make three scenarios for this game: Q 1st, Q 2nd, and Q 4th.

I normally don’t make more than two upfront scenarios. But, when there is a strictly defined set of scenarios like this, it can be very efficient to make three. Scenarios tend to be much faster than simply using the rules. However, unusually for a scenario based game, you also have to remember the rules very well when examining the scenarios. That’s part of what makes this game difficult.

Before making the scenarios, let’s get clear on our rules. G and H need the same investigator: we can use an X to mark this. And, G and Ikaba can’t be consecutive:

I’ve also written the deduction that Q can only go once, as it will be important not to draw Q twice in any scenario. We could draw “QF”, but we’ll have that in the scenarios, so it’s not necessary.

Now, let’s make the scenarios, starting with placing QF first. Remember, when we’re making the scenarios and have placed Q, we only have two rules left. G and Ikaba are separate, and GH have the same investigator. So on any question all you have to do is draw the appropriate scenario then run through those two rules.

How to Build These Scenarios

It’s very possible that these scenarios will seem confusing if you just read them. So, I’d encourage you to build them yourself. Here’s how. Do the following for each placement of Q:

1. Place Q. In scenario 1, place Q 1st. In scenario 2, place them 2nd. In scenario 3, place Q 4th.
2. Place G and Ikaba separate from each other (rule 2). But draw a line to show they’re reversible.
3. Place the investigators. If either G or H is 3rd, then R interviews both G and H (rule 1 + rule 4). If instead Ikaba is third, then R interviews Ikaba and S interviews G and H.

Fiddle around with making these scenarios while reading the explanations and hopefully they’ll make sense. Make concrete examples placing G and Ikaba in definite spots to help it click. This kind of scenario construction under uncertainty but within the constraints of the rules is key to advanced logic games.

Scenario 1: Q first

If Q/F is first, then H has to go third in order to separate GI (rule 2):

The curved line shows G and I are reversible. So if a could be true question asked “could G go fourth”, this diagram would prove it could.

The only rule left is that GH have the same investigator. We can draw that with a subscript. H already has R, so G has to be interviewed by R too (rule 1), and Ikaba by S (because every investigator has to go at least once):

Scenario 2: Q second

For the next scenario, place QF 2nd. This leaves us with an open spot in 3-4. We can’t place GI there: they must be separate (rule 2). So one of GI goes there, along with H. The other GI goes first:

The comma between H, G/I tells us that H and G/I can go in either order. And I used x subscripts to remind us that GH have the same investigator, no matter where they are placed.

So, for example, if I is 1st, and HG in 3rd and 4th, then I is interviewed by S, and HG are interviewed by R (because R is third, and because both H and G need the same interviewer).

So, this scenario is a bit more open ended than scenario 1. But once you place Ikaba, it becomes quite clear how to place the rest and/or who investigates them.

Scenario 3: Q is fourth

Next, scenario 3. Q and F are fourth. This is like scenario 1: it forces H in the middle of G and I to keep them apart (rule 2):

G and I are reversible. The x’s indicate that H and G will have the same investigator. So, for example, if I goes third, then GH will have S. If I goes first, then GH will have R.

That’s it for this game. Here are the three scenarios all together:

These solve basically all the questions. Remember the outstanding rules:

1. GI don’t go together.
2. GH have the same investigator.
3. F only goes once. S needs to be placed.

I should also note that all three scenarios are valid and can obey the rules. But in some games, there are scenarios that seem possible at first, but don’t produce a valid scenario. So, it’s worth testing the scenarios a little to make sure they obey the rules in case you’re not 100% clear on how a valid scenario can be formed from the above drawings. (By valid scenario, I mean one where all the witnesses and investigators have been placed into a definite position on the board)

What if these scenarios don’t make sense

Rereading this explanation, I found it confusing to explain in writing. But, I have confidence these scenarios will make sense if you try them, and they aren’t overcomplicated to actually use. So, I recommend you try these scenarios on some questions and see how they work with examples, and then redo this game and use them.

Key Relationship: who interviews G and H?

If G or H is placed third, then both will be interviewed by R. Whereas if I is placed third, then GH will both be interviewed by S. This rule applies in all scenarios.

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