Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Pure Sequencing game.

The seven rules combine to form the following diagram:

Feb92_Game_#1_setup_diagram 1.png

The relationships are not overly complex, and in analyzing the diagram two important facts are clear:

• *K must have the highest salary.
  
  *Either H or N or both must have the lowest salary.

Given the simplicity of the diagram, you should make a quick analysis of the relationships, and then swiftly move to the questions.

[Makar]

Hello,
I have a question regarding number 2 on this game. It asks, “ if Mallory and Nassar earn the same salary at least how many of the partners have lower salaries than Lopez?” My question is, I got the first question right because I answered it assuming each person has only one slot. However if number 2 changes that, doesn’t that allow for a different answer for number one and basically for all the answers? Also if number two says Malloy and Nassar receive the same salary technically when trying to answer, couldn’t you put others as having the same salary as well. Lastly, for number 5, it asks “ what is the minimum number of different salaries earned by the nine partners of the firm.” How many can we assume would can have the same salary? Could it be 3?
Thanks,

Alex

[Adam Tyson]

Here's the problem, Alex:

I answered it assuming...

You should never make any assumptions about what is true in a game! You should just apply the rules as they are given! While it must be true that each person has exactly one salary (how can someone at one job have multiple salaries? That would be nonsensical.), it is NOT required here that each person's salary be unique. Some of these people could be making the same salary as some other people. Not everyone can be tied, but some can.

We do have to follow the rules, of course, and M cannot be third (Question 1) because K, I, and F must all make more than M. None of them can be tied with each other because the rules say that K makes more than I, I makes more than F, and F makes more than M. Any possible ties will not be found within a chain (K-I-F-M-G-J-H is one chain, and K-L-N is the other chain, with K as the only common variable) but BETWEEN the chains. L could be tied with anyone except for K, who must make more than L, and N, who must make less. So L could make the same as any one of IFMGJH. N can be tied with anyone other than K and L, because those two have to make more than N. So N can be tied with any one of IFMGJH, just like N could.

The information in question 2 about a tie between M and N doesn't change the rules or the answers to any of the other questions, but rather presents one possibility that is within the original set of rules. We cannot change the rules and say that, for example, G and J might be tied, because the rules clearly state that G makes more than J.

As to question 5, to get the minimum number of different salaries, you have to imagine that L is tied with someone else and that N is also tied with someone else. Those are the only possible ties, so at that point you are left with 7 different salaries. Picture, for example, L tied with I and N tied with F. No other ties are allowed by the rules, and so you have 9 people but only 7 salaries. There is no way to get fewer salaries because nobody else is allowed to have ties, and any attempt to make them have ties would break a rule.

Don't assume anything! Follow the rules as they are written, and anything that is not against the rules is allowed by them!

[concrottrox11@gmail.com]

Hi,

Why are the variables after I and L not on a diagonal in this problem and instead linear to each other? This particularly stumps me when looking at (F M G J H) after I and (N) after L. Shouldn't they be on diagonals because they have no further relations with each other?

Please let me know your thoughts. Thank you!

[Robert Carroll]

concrottrox,

Start with the third rule: I is before F, F before M, M before G, G before J, and J before H. If all that's true, the relationships shown on the diagram ARE true - I is before M, I is before G, I is before J, I is before H, F is before G...and I could keep going. In general, in Pure Sequencing games, variables have a relationship under either of two conditions:

1. There is a dash going directly from one variable to the other (for instance, I F here)

2. There is a path of dashes connecting the two variables with no change of direction (I F M G J H provides, among many others, a path from I to H which maintains its direction. Therefore, I H).

Diagonals would be fine, but not change anything at all about the relationships represented.

I hope this is clear. Let me know if you need any more help!

Robert Carroll