#11 - Global, Must Be True, Maximum

[mshaikh]

After looking through majority of the answers on here I am still very confused. I had my set up right, but especially this question still confuses me. I put A for the answer choice and I don't get why that is wrong. It makes sense that L,J, and P could all either be top 3 but it doesn't make sense to me for N to be included. I thought that J or L must have received the most votes so don't they have to be the first two in the line up??? I am thinking either J will be first or L will be first, meaning one of the two must be second. Also the diagram provided here says this, "Either L or J must have received the most votes." What am I not understanding? I do sort of understand that we don't know the exact relationship (vote difference) between J and N, but how does that make N a possibility for one of the top 3? Please help!

[Adam Tyson]

I get your confusion here, mshaikh, and it's a common mistake to believe that since only L and J can be first, then once one of them is selected for first the other must be second. But while L and J are the only ones that can be first (because they are the only ones that do not HAVE to have something in front of them), once you place one of them first the other one becomes a little more free to move around.

Now granted, if J is first, L has to be second, because nothing else can be. L must come before every other variable in the chain, right? But J isn't quite so restricted - it only MUST be before O, K, and M, in that order. If I put L first, the order could be LPNJOKM, with N in the third position (and thus being one of the four variables that could be in the first three). What rule does this violate? J is still before O, as required. L is before P, and P is before N and also before O. There's no problem here!

As long as we are not breaking a rule by putting N before J, it isn't prohibited, and that's how we can come up with the correct answer here, answer B.

Let us know if that doesn't do the trick for you. Keep up the good work!

[mshaikh]

That makes sense a lot more sense! I didn't understand that J was way more flexible than L so now I understand that the answer to this question would have to be 4. Thanks for the clarification Adam!

[Jon Denning]

Was asked about this yesterday by one of my students, so wanted to put my reply in here for other readers.

This question is just asking how many of the seven drinks can we have go in the first three spots. So simply think about what would prevent something from going in spots 1-3: three or more things in front (to the left of) it. And now we can just count them out. J can go in the first three, as it has nothing to its left. Ditto for L. P can also go into the first three (not first, but either second or third, after L). And N can also go in those first three spots, as long as L is 1 and P is 2 (that would also put J O K M in 4-7). But what about the other three, O, K, and M? Well O has three things minimum ahead of it, L, P, and J. So it can’t go any earlier than 4. K has at least four things in front of it: J, L, P, and O. So we can put K in 5 at the earliest. And M is always last (since N can’t be), so it’ll never be in 1-3.

So we have four different variables—J, L, P, and O—that can be in the first three spots, and that’s why answer choice B is correct for #11.

[whardy21]

Can you please explain how N makes it into the top three.

[Malila Robinson]

Hi Whardy21,
As Jonathan previously mentioned your chart for this game should look something like this:
L
|
P J
/ \|
N O
\ |
| K
|/
M

So, to get N in top three you can use L-P-N. But L-P-J and L-J-P also works, which is how you end up with 4 variables, L, J, P, N.
Hope that helps!
-Malila

[lizaetillman]

I chose (a) because I missed that N can also be in the top three. I'm a little nervous now. After reading the reasonings above, seemed so simple -- but I didn't catch that.

[Robert Carroll]

Liza,

It is tricky, and one of the things that can be difficult (at first) about sequencing notation. To tell whether a given variable can be among the first three, consider the question "How many things must be before this?" Very often, a variable may have the possibility of having a lot of things before it, but doesn't need more than two before it - so it can be among the first three.

Robert Carroll

[Kims1737]

This is one of the 1st questions in the course of pure sequencing in the book and I'm needing some help understanding the logic behind the letters that branch off with nothing in front of them, in this case J and N. I've heard it explained but don't understand how they can be supersede others when the "appear" to be behind the other letters. Or in this case would have less votes since they are behind Luck, Ping and Oboy. I got lost in your explanation about all the letters as opposed to the actual soda as it relates to votes? Can you answer as it relates to "votes"? That would be super helpful. What does it mean for the letters that hang off and their positioning for all of these questions going forward?

[KelseyWoods]

Hi Kims!

Remember that in Pure Sequencing setups, you cannot rely on the physical proximity of variables on the page to determine whether they are before or after one another--you have to rely on the actual relationships. When you look at J on your diagram, are there any links before it? Any lines connected to it that say something has to be before it? Nope. So that means that there is nothing that has to have more votes than J, which means J could have the most votes. When you look at N, what has to be before N? It has a direct link to P before it (meaning P gets more votes than N) and a direct link showing that L is before P (meaning L gets more votes than both P and N). So N has to have at least 2 sodas that receive more votes than it. J is to the left of N on our diagram, but do we know how J and N are related to one another? Does J actually have to receive more votes than N? No, because we don't have any direct links between J and N.

Try it this way: Looking at your diagram, put your finger on J. Now travel from J to N, only following the links between your variables. What happens? To get from J to N you have to go forward from J to O, then backward from O to P, then forward from P to N. If you have to travel in multiple directions (forward AND backward) to get between 2 variables, then you can't actually make any inferences about how those variables are related to one another. With J, you can travel forward to O, forward to K, and forward to M. So you know that J receives more votes than O, K, & M because you are only traveling in one direction (forward) to get from J to any of those variables. But to get from J to L, P, or N, you would have to travel forward to O and then backward to P. That's 2 directions (forward and backward) so you don't know how J is related to those variables. J could be before L, P, and N, it could be after L, P, and N, or it could be between L and P or between P and N. There are no restrictions on how they are related to one another.

Hope this helps!

Best,
Kelsey