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Dave,
My question is regarding two placeholders in this specific example. I know why K/J are a placeholder, but why is the second placeholder (I know why it's there) N/L instead of P/L. N and P are on the same side of the equation, why did you choose N? Is it because P is alone in the last rule?
It's the same case with the K/P placeholder... I know there's a placeholder there but couldn't it just as easy have been O/P?
I realize it's not necessary for the questions asked, but is it safe to assume L is always out based on the rules?
What's super useful about this question is to think abou thow we'd go about testing it.
Here's what you do: put L in, then go down your list of rules, applying each one. If you have to break a rule to make it work, then L must be out!
Hey Dave, I don't seem to be able to find the Min/Max number video you referred to in the video. Was just wondering if you could post the link? Thanks!
I can't find it either!
WHAT THE HECK HAPPENED TO MY GOLDARNED MIN/MAX VIDEO, LOUISHAWK94?!?
I'll see if I can find it on my end and upload again and post a link, or I'll record a new one. Sorry about that!
I was searching for this min/max video and couldn't find it. Did I miss it in the theory videos/ is there a link?
Thanks so much!
Well, this is embarrassing for me. It looks like we somehow lost that video years ago (probably the last time we switched websites), and another student asked me about it, and I said I'd find it and re-upload, and then I... just didn't. Face palm.
Fortunately, the idea is pretty simple, so I'll just sketch it out for you here, and add a new min/max video to my list of todos.
Here's what I do with minimum or maximum number questions (I'll start with minimums, then we'll look at maximums):
I do not try to think about what the minimum might be. I don't try to start from the smallest number. Instead, I start from my prior work, and I do not lose sight of my placeholders.
Here's the process, using PrepTest 34, Game 4, Q 21 as an example:
1. Eliminate options based on placeholders. Here, for example, we know from our placeholders that we'll never have fewer than 2 doctors at Souderton, so we can get rid of (A) and (B) straightaway.
2. Use prior work to eliminate other bad options. For example, we've seen as few as 3 doctors in the answer to Q 20, so we can eliminate (E).
3. Finally, start from the smallest number you've ever seen in prior work, then ask whether you can make that number even smaller. For example, if you had tried out answer choice (C) in Q 23 before answering Q 21, then you would know that it's possible to have only two doctors at Souderton. On the other hand, if you hadn't done that question yet (or if you got it without trying out (C)), then you'd start with the smallest number you'd seen before. There are only 3 doctors (N, K, and O) in Q 20, so I'll start from my work for that question.
Because I physically (visually) use my placeholders, I can see that moving K or O out will profit me nothing; I'd have to replace them with P or J, respectively. So if I want fewer than 3 doctors, I need to move N out. If I can do that successfully (i.e., without breaking any rules or adding any more doctors), then I'll know the smallest number possible is 2.
And we can! If we move N out, that takes O out. If O is out, then J is in (so now we have _ J | _ _ N O)
J kicks out K, and when K is out, P is in (giving us P J | K _ N O)
Finally, when P is in, L is out, so we can have as few as two doctors (P and J) at Souderton, while everyone else is at Randsborough.
[Note: if you wanted, you could skip steps 1 and 2 and do the entire question using only step 3. Sometimes, though, you'll get all the way to the right answer by using only steps 1 and 2, so I've included them here because they're not much work to do].
Maximum questions (let's use this same game, and pretend that Q 21 had asked for the maximum number of doctors at Randsborough, and that the test writers had given us options (A) 6; (B) 5; (C) 4; (D) 3; and (E) 2):
1. Eliminate options based on placeholders. Here, for example, we know from our placeholders that we'll always have at least 2 doctors at Souderton, so we can never have more than 4 at Randsborough, and we can get rid of (A) and (B) straightaway.
2. Use prior work to eliminate other bad options. For example, we've seen as many as 3 doctors in the answer to Q 20, so we can eliminate (E).
3. Finally, start from the largest number you've ever seen in prior work, then ask whether you can make that number even bigger. For example, if you had tried out answer choice (C) in Q 23 before answering Q 21, then you would know that it's possible to have only two doctors at Souderton, leaving a maximum of 4 at Randsborough. On the other hand, if you hadn't done that question yet (or if you got it without trying out (C)), then you'd start with the largest number you'd seen before. There are 3 doctors (J, L, and P) in Q 20, so I'll start from my work for that question.
Because I physically (visually) use my placeholders, I can see that moving K or O over to Randsborough will profit me nothing; I'd have to trade P or J to Souderton for them. So if I want more than 3 doctors, I need to move N to Randsborough. If I can do that successfully (i.e., without breaking any rules or losing any more doctors), then I'll know the largest number possible is 4. And, of course, we can move N from Souderton to Randsborough, in exactly the same process we used above.
That's it! That's the process.
Make sense?
Yes! This helps so much! Thanks for writing out the steps, I can apply these process to other games. I felt I was tracking with you in the video--but then when you mentioned an additional video, I was like did I miss something? lol. But this explanation cements the process further and is a great help. Thanks again for taking the time to write it out, I will def be returning to this game for review. :)
I tried putting an awesome gif here, but it didn't gif, so instead I'll ask you to imagine a fist pump and a fricking sweet "Yessss!"