Maximum/Minimum Questions

cmelman95

I've noticed that one of my big problems with LG (and there are _many_, are maximum/minimum questions. For example, "the maximum number of Bs that can be in group F is___?" These questions are difficult for me because it's tough to know when I'm getting them wrong. In other words, I don't know when I've done all I can to get to the solution. Now, you might just say, "Run down your rules and make sure you haven't failed anything." Right, OK, but sometimes you do that and you still haven't maximized or minimized because there are other valid solutions that contain more or less of the variable in question. Unfortunately, I don't find JY's videos particularly helpful here because it seems like he just sees the best way to do the problem (and/or he has the benefit of hindsight and an answer key). Are there any actual strategies I can use here, or am I at the mercy of my intuition?

MrSamIam

Look at the answer choices. If it's a "maximum" question, test out the highest number first. Then work your way DOWN (second highest, third highest, etc.).
Do the opposite for "minimum" questions. For me, that's the most efficient way to approach those questions.

as5324therapy

Min--count your "or" rules
Max-count your "not both" rules

Nanchito-1-1

If it says there is a max or min, than perhaps there are more than one diagrams where a position/entity is fixed. Try drawing more than one possibility and figure out as many inferences as you can. Then look at jy's explanation and try to follow his reasoning for what he's doing and why. Then do it again and again until it burns in your brain.

runiggyrun

Hi @cmelman95. The strategy on attacking the questions depends on what type of game it is.
For a simple sequencing game with a tree diagram, if the question asks "what's the maximum/minimum number of elements that could come after/before B", you have to look at your "tree diagram" and see how many "followers" B has (they have to come after) or how many leaders (they have to come before).
This sort of question can appear as "what's the earliest/latest slot B can have" "how many people can be scheduled before B but after A", etc.
For some of the more weird sequencing-type games (a circular one comes to mind, as well as another about professors and rooms, but there are others), you do what @MrSamIam suggested and work your way down from the highest number for a maximum and up from the lowest for a minimum and see what's the first number where you can fit everything on the board without violating any rules.
For grouping, or in/out games, you should be able to tell without having to draw hypotheticals, but it's not easy without a lot of practice.
You have to be very mindful of the floaters, which can go anywhere, and your "at least one" and "not both" rules. It often helps to write them right on your board (So, if you have a A-->B (not both rule) you know that the "out" group is going to include either A or B, so at least one of those is out. Write an out slot filled with A/B, to keep track of them.
If you have 6 elements and two of these rules, you look at your board and know that at least two elements have to be out, so you can't have more than 4 in.
If they also throw in a C-->D rule (at least one rule), you fill the "in" group with a C/D slot. So you know you can't have less than 1 in.
This sort of thinking should be able to eliminate at least some of the answer choices and give you a pretty good idea of what the one or two most promising ones for trying out would be.
These are tough questions, and until you get very comfortable being able to see how many "not both" and "at least one" rules you have, they would be good candidates for skipping under timed conditions and coming back to them if you have time.