Assume that the partners of the firm are ranked according to their salaries, from first (highest) to ninth (lowest), ...

Juliana on June 5, 2019

Question 6

I understand how Glassen can be fifth and seventh but I am not really understanding how he can also be sixth. If the order goes from K to I and L (same column) then I to F, L to N, then F to M and so on for the rest of the line, why would you only count K, I, L, F, M and not K, I, L ,F, N, and M? since both I and L are in the same column and F and N are? Hopefully that makes enough sense.

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Ravi on June 7, 2019


Happy to help.

We know that K is in the first position, and we also have these two
chains from the information in the rules:



K_ _ _ _ _ _ _ _

The question asks, "Assume that the partners of the firm are ranked
according to their salaries, from first (highest) to ninth (lowest),
and that no two salaries are the same. Which one of the following is a
complete and accurate list of Glassen’s possible ranks?"

Because there are no ties, we know there are nine slots since we have
nine game pieces. Based on our chains, we know that G has to be lower
than K, I, F, and M, so the highest G could possibly go is 5th. We
also know that G has to be higher than both J and H, so the lowest G
could possibly go is 7th. Could G go in 6th? Well, if we give L a
higher salary than G, then G could go in 6th since it would have 5
pieces before it. It would be fine if L had a higher salary than G
since the only relationship L has is with N (going before it).

From this, we know that G could also go 6th if there are no ties, so
(D), which states that G could go 5th, 6th, or 7th, is the correct

Does this make sense? Let us know if you have any more questions!

Emily on July 9, 2020

I am still a little confused on why we did not include N. In the rule, it say L is tied with N, so once we put L in our new chain for this problem ( K-I-L(N)-F-M-G-....), why didnt we include it after L. instead, when i watched the video explanation, they put it after G

on December 19, 2020

I think we don't include N because we're asked to see if it's possible for G to hold a place. We don't have to disprove anything here (which is what I think adding N would do). We're trying to do the opposite (just prove that it can work out in a case) so that is why we intentionally leave out N and place that after G because there's no rule telling us that we can't do that.