Diagramming Grouping Games trouble

[TargTru99^]

Greetings,

I have run into a struggle with diagramming grouping games, particularly for Game #2 on p. 5-14 of the live online prep course books and on #4 on the drill on p. 5-89. On #4 on p. 5-89, I made the mistake of making the DFG variables as the groups for where the variables STVWY would be placed in. The answer key for the drill showed that the five variables of the lab assistants in the game had to make up the grouping base instead. How do I avoid this mistake?

Also, when attempting Game #2 on p. 5-14, the inferences I made from the rules did not help enough me to correctly answer the first question of the game. The best inferences I came up with was Lr Pj, not Pj not Lr, not Pj Lj, and not Lj Pj. I also symbolized the last rule by putting F in a single block square and drawing it as a single square not block. I also do not understand why F or S must be placed in for G as a result of the second rule, which is what is asserted in the forum explaining the setup for this game (link:lsat/viewtopic.php?t=13972). Please explain that to me, as I do not understand why F and S cannot be placed in group J or R.

[Adam Tyson]

Thanks for the question, TargTru99^. Selecting the best base in grouping games can be tricky at times, but often the key is to focus on the numbers. Rules that place numeric restrictions on variables often point the way to those variables being a good base, because those restrictions end up establishing the size of the groups. That drill on page 5-89, for example, tells you exactly how many solutions each assistant tests. In addition, the scenario tells you that each assistant tests at least one of the solutions. If we use the assistants as the base, we know that there is a minimum of one solution per assistant, even before we get to the part about exactly how many they each test. Since we can fix in place the numbers for the 5 assistants, but the solutions remain unknown (how many assistants have to test D? How many must test F? etc.) it is helpful to make the assistants the base. The same idea can be applied to the game on page 6-4, when you get there - focus on the variable set that has the most numerical restrictions, and make that set your base.

In short, numbers often determine the base. Groups of fixed or limited size are easier to deal with than ones that are very flexible.

That's also one of the driving factors in the game on page 5-14, with the housemates getting mail. The housemates must each get at least one piece of mail, and the housemate getting F has to get more than that. Those two rules place numeric restrictions on the housemates more than on the mail, so the housemates make a better base.

As to that inference about F or S going to G, that isn't a global inference that must always be true. Instead, it is tied to the second rule - if L goes to R, then P must go to J. Now, consider G in this scenario - she has to get at least one piece of mail. She can never get L or M, per the first rule, and in this scenario she also cannot get P, because that is going to J. What's left? Only F and S, so G has to get at least one of those. Now, couple that with the rule that F cannot be alone, and G has to get S in this case. G either gets S alone, or S with F. Otherwise, G gets nothing, or else breaks the rule about F. That's an inference that a lot of folks might miss, but it's worth trying the hypothetical based on the second rule to figure it out.

In a different scenario, G could get neither F nor S. What would she get, then? She would have to get P, the only thing left she is allowed to have. With P going to G, L would have to go to J (good job making that inference!), and MSF can be distributed between P and R several different ways. It's only when P goes to J that G must get S. That's why F or S going to G is not a global inference, but merely a conditional result of L going to R.

When in doubt, try playing with a hypothetical or two, and you may make a few key inferences that way. I hope that helps!