Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping: Partially Defined, Numerical Distribution game.

The first sentence of the scenario establishes that either 5 or 6 works will be selected:

PT32-Oct 2000 LGE-G2_srd1.png

Because the game is Partially Defined at five or six works selected, the diagram above shows that at least five works must be selected; the bar between the fifth and sixth work indicates that a sixth works can possibly be selected.

The second sentence establishes that the group of nine works is composed of French and Russian novels and plays. As each work has two characteristics, one method is to show them in a vertical format:

PT32-Oct 2000 LGE-G2_srd2.png

Thus, our diagram should also have two rows, one for the nationality and one for the type of work:

PT32-Oct 2000 LGE-G2_srd3.png

The first three rules each address a numerical aspect of the game. The first rule indicates that at most four French works are selected, meaning that at least one Russian work is selected. The combination of the second and third rules creates four basic Numerical Distributions for FN and RN:

PT32-Oct 2000 LGE-G2_srd4.png

Other seemingly possible numerical combinations of FN and RN, such as 3-2 or 3-3, are impossible because the maximum number of novels is 4. Combinations such as 1-0, 1-1, and 2-0 are impossible because they would cause fewer than five total works to be selected.

These four distributions indicate that at least two FNs must always be selected. Also, since the maximum number of novels is four, at least one P must always be selected. The two FNs can easily be shown on the diagram, and then the choice is yours as to show the minimum one P or the minimum one R. Here is the diagram with both FNs, the minimum of three Ns, and one P:

PT32-Oct 2000 LGE-G2_srd5.png

The four FN/RN distributions have a powerful effect on the questions. For example, on question #8, the distributions show that answer choice (A) could be true and is therefore correct. On question #10, the distributions prove that answer choice (D) is correct. The distribution even has an impact on question #11 as it shows that answer choice (A) is impossible: if no RNs are selected, the maximum number of FN’s selected is three, and three FNs plus exactly one P equals four total works, one less than the required minimum.

The last rule of the game states that if both FPs are selected, then no RP is selected. But, because at least one R work must be selected, if both FPs are selected then at least one RN is selected:

PT32-Oct 2000 LGE-G2_srd6.png

Consequently, at most two plays can be selected, which corresponds to the second rule that at least three novels are always selected.

Overall, the rules in the game are not precise, and thus they are not easy to display conventionally. This situation gives the game a piecemeal or random feel. However, if you can focus on the rules involving numbers and thereby create the FN/RN distribution, this game is not difficult. Here is the final diagram for this game:

PT32-Oct 2000 LGE-G2_srd7.png

[srcline@noctrl.edu]

Hello

Can someone please explain how to set up this game, the entire stimulus and rules is confusing for me, is this a grouping game? The only inference that I got was that a russian play and both French play can never be selected together i.e a double not arrow. Is this correct.


Thankyou
Sarah

[Emily Haney-Caron]

Hi Sarah,

Yes, this is a grouping game; you're concerned with which variables are "in" and which are "out." You are correct that a Russian play can never be selected with both French plays, so you cannot ever have more than 2 plays. The other big inference here is that you will have 2-3 French novels, because you will have 3-4 novels and there cannot be more Russian novels than French novels.

If there are only 3 novels, you will only have 5 works total, because you can't have more than 2 plays.
If there are 4 novels, you can have either 5 works total (1 play), or 6 works total (2 plays).

That allows for templates:
1: you have 3 novels (2 of which must be French) and 2 plays (1 of which must be French)
2: you have 4 novels (2 of which must be French) and 2 plays (1 of which must be French)
3: you have 4 novels (2 of which must be French) and 1 play (which can be French or Russian)

Try working with that set-up and see if that helps with the questions.

[srcline@noctrl.edu]

Hello, Emily

I am still a bit confused. I understand the double not arrow, but I am not how there are going to be 2-3 french novels, and will have 3-4 novels and there cannot be more Russian novels than French novels. I think I'm having trouble with the third rule that states that "at least as many french novels as russian novels are selected? Isnt this saying that there has to be an equal amount of novels selected b/w french and russian?

Thankyou
Sarah

[Jon Denning]

Hey Sarah,

Thanks for the followup! Let me see if I can clarify this for you.

The third rule is a little tricky, since it's not absolute like many rules are (it doesn't specify exactly how many French or Russian novels are selected). What it tells you is that, as you state, there can never be more Russian novels than French novels, so you could have the same amount at 2 novels each, or you could have more French with either a 2:1 or a 3:1 French:Russian split, or all the novels could be French if only 3 novels are selected. So a lot of variability there.

What might be confusing you in Emily's reply is that in each template where she states how many novels must be French, what she really means in most instances is that "at least X of which must be...," rather than an exact number. So to hopefully make that more clear, here's her three template options with slightly altered wordings and order:

1: Five total works, with 3 novels (at least 2 of which must be French, and possibly all 3) and 2 plays (at least 1 of which must be French, and possibly both as long as there's a Russian novel)

2: Five total works, with 4 novels (at least 2 of which must be French, with the possibility of 3 French) and 1 play (which can be French or Russian)

3: Six total works, with 4 novels (at least 2 of which must be French, with the possibility of 3 French) and 2 plays (at least 1 of which must be French, and possibly both depending on the number of French novels)

You'll note that the first rule constrains some of those, since you can only have a maximum of four French works. So for template #3, for instance, if you have 3 French novels and 1 Russian novel, then you'd have to have only 1 French play (total of 4 French), and the other play is Russian. If the novels are split 2/2 between French and Russian, then both plays could be French.

I hope that helps!

Jon

[lathlee]

Hi. I believe this game 's difficulty, fair to be considered in one of the Honorable mentions of Hardest 12 LG Ever, considering coming up proper set up would be pretty difficult and if this one doesn't come up proper setup, the game's level goes up to hellish.

[LSAT2018]

How would this game be drawn out? Because of so many variables at play (the group consists of three French novels, three Russian novels, two French plays, and one Russian play) is there an efficient way to diagram this?

[Vaidehi Joshi]

@LSAT2018,

Your intuition is right--there are a lot of variables at play, and a lot of possibilities, so this game's diagram isn't going to be the most efficient, and it's going to be a very rule-driven game.
Like Emily said, it's going to be a grouping game with an "in" and "out" group. You may or may not choose to have classification rows of French vs. Russian in your diagram--I chose not to. I think it's best not to, since I didn't find that very helpful. I instead used variables with subscripts (French/Russian as the main variable, Novel/Play as the subscript) but I know some folks hate keeping track of variables with subscripts.

It's hard to represent super well over forum typeface, but see Image 1 for how I set up my game board.

but because we are told we have min 5, max 6 selected (in the IN group), we can infer the following:
-since there is min 5, we must have 5 slots under IN. you can write in 5 slots.
-since there is max 6, meaning at least 3 out (9-6=3) we can write in 3 slots under OUT
since that's 8 total, we have 1 more "floater" slot that can go in either in or out. just keep that either in mind or in the space between the two groups:
(see Image 2)

then you can fill in more constants to the diagram with the aid of the rules:
-No more than four French works are selected-->but since we have to have min 5 in IN, then we know at least one of them with be Russian. so you can put an RN/P into the left side of the game board
this also implies that you have at least 1 French work OUT, since you have 5 French total. so you can put an FN/P into the right side of the game board
At least three but no more than four novels are selected --- you can make a note to the side that says "3-4 N" or something. this also implies that at least 2 Ns will be out. even if your FN/P were a novel, you'd have to have one more necessarily out. thus, you can fill in just the subscript N into another line on the OUT side of the diagram.
At least as many French novels as Russian novels are selected. just make a note to the side "FN>RN "
so it'll look more like: (see Image 3)

[yenisey]

The third rule states: " At least as many French novels as Russian novels are selected.". Does this sentence mean French novels are equal to Russian novels or it means there are more French novels than Russian novels?

[Robert Carroll]

yenisey,

"At least as many French novels as Russian novels are selected" means that the number of French novels will be equal to OR greater than the number of Russian novels.

Robert Carroll