Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping/Linear Combination, Numerical Distributions game.

At first glance, this game appears to be a simple Basic Linear game:

PT30-Dec 1999 LGE-G2_srd1.png

However, the first and second rules indicate that this game is not Balanced, opening up a host of numerical possibilities. These possibilities ultimately make the game much more difficult.

PT30-Dec 1999 LGE-G2_srd2.png

We will reconsider these distributions once the remaining rules have been analyzed.


The third rule establishes a basic conditional relationship:

PT30-Dec 1999 LGE-G2_srd3.png

The fourth rule is also conditional, and it indicates that when G leaves a message, so do F and P:

PT30-Dec 1999 LGE-G2_srd4.png

The fifth and sixth rules are similar. Both are conditional, and include sequential information:

PT30-Dec 1999 LGE-G2_srd5.png

One of the critical inferences of the game is initiated by the combination of the fourth, fifth, and sixth rules:

PT30-Dec 1999 LGE-G2_srd6.png

The diagram above indicates that if G leaves a message, then every other variable must also leave a message. Thus, since the first two rules create several Unfixed Numerical Distributions, the composition of the people leaving messages under each distribution can be determined:

PT30-Dec 1999 LGE-G2_srd7.png

PT30-Dec 1999 LGE-G2_srd11.png

H, L, P, and T always leave messages. Because P must always leave a message, and thus H > L, L can never leave the first message and H can never leave the sixth message.

This is the final diagram for the game:

[moshei24]

This game took me a long time to complete, and only after completing it did I realize the following.

There are only three possible distributions:

#1: G, F, P, T, H, L (P>T; H>L)
#2: F, P, T, H, L (P>T; H>L)
#3: P, H, L, T (H>L)

H can only be first in the 3rd distribution. H, L, and T always have to leave messages.

Is another inference knowing which of the people in the each distribution can have more than one message? Or are those the main inferences in this game?

Also on #7, does the fact that someone's second message is last imply that we're dealing with distribution #2? Which would imply that P, T, H, and L cannot be both first and last because they all need to either have someone before or after them?

Thank you!

[moshei24]

I just realized that I misread a rule.

Two more distributions are:

#4: P,H, L
#5: H, L

So only H and L always need to leave messages. And H can also be first in the 4th distribution.

Is it just me or is this game an extremely difficult game?

Thanks for the help!

[Dave Killoran]

Hi Moshe,

I've always thought this is a deceptively hard game. It's linear with some sequencing, and that usually seems easy, but they throw everything for a loop when it turns out that someone can leave more than one message (and thus not everyone has to leave a message).

I'm not sure about the distributions you created (especially #4 and #5--are you saying that just 3 or 2 people left messages? That's not possible). I actually prefer to set this game up by looking at the distribution of number of messages to people. There are three Numerical Distributions under that framework:

• 1. 1-1-1-1-1-1
  
  Here, each person leaves exactly one message, and all variable-specific rules are in effect (P > T, H > L). The possibility of a distribution such as this one answers question #9.
  
  
  2. 2-1-1-1-1-0
  
  One person leaves exactly two messages (and thus this is the distribution in play for a question like #7), four people leave one message each, and one person leaves no message.
  
  In this distribution, everyone leaves a message except G (thus, G is the "0" above). If G is selected, every other variable must also be selected, thus, if someone isn't going to leave a message, it has to be G.
  
  
  3. 3-1-1-1-0-0
  
  One person leaves exactly three messages, three people leave one message each, and two people leaves no message.
  
  In this distribution, everyone leaves a message except F and G (thus, F and G are the "0s" above).

In every distribution, at least P, T, H, and L leave messages.

Please let me know if that helps. Thanks!

[moshei24]

Looking back on it now, my first analysis of the game was accurate and was the same as your analysis, just written differently. When I had written that I had misread a rule, I was incorrect about that, and I had actually read the rules correctly the first time.

Thank you for clearing that up for me.

I think one inference I mentioned that you did not mention was that H can only go first in the 3rd distribution. In the other two, he can't go first, because then P is forced to go last, creating a problem, because T has to go after P.

[Dave Killoran]

Yeah, I wasn't trying to note the positional inferences, but that is correct about H. You could go on to add that H can never be sixth and L can be first, because P always leaves a message, so the last rule is always in effect.

Thanks!

[moshei24]

Right, right. Thanks!

[Johnclem]

Hello Dave ,
Just a quick question about this one . A few of my friends from other prep companies have shown me to link all the conditional staments into a chain ,like how we would with sequence games. The issue I'm having with this is that if G is selected then we have F and P selected ( like grouping games )but how do we know their relative positioning to one another ? I see the sufficiant triggers which means G sufficient but we've never done this with grouping games .. link them up I mean . so I find it odd to do. It was faster for me to solve the game . I just don't know if I shoukd make a habit if it .


Thanks
John

[Kristina Moen]

Hi John,

You are correct that if G is selected, then F & P are selected, but we don't know their relative positioning. One way to diagram this is by using for conditional statements and for positional (linear) statements.

So here, you can diagram "If Greta left any message, Fleure and Pasquale did also" as G F and P.

You can also diagram "If Fleure left any message, Pasquale and Theodore did also, all of Pasquale’s preceding any of Theodore’s" as F P T (both selected)

You can combine those rules pretty easily because P shows up in the necessary condition for F as well.
G F P T (both selected)
You can also draw diagrams with conditional statements branching off.

So the contrapositive tells you that if P does not come before T (or neither of them are selected), then you can't have F, and then you can't have G. So this also tells you that if G is selected, then 3 other variables must be selected. Of course, once you add the last rule, you find out that if G is selected, then every other variable must be selected too.

[yrivers]

Hi,

I had a question on the contrapositive of the game's rules.

F --> P - T

Looking at the rule above, if I don't have P (in other words, P is out), how does that mean there is no F? I understand F --> P very clearly, but for some reason I am getting confused with the P-T piece. What happens when P is out and when T is out? I think in both cases, it means that F is also out. Hence in the game, you MUST have P-T in the game. And same with H-L.

I guess I don't understand how if T is out, you can 100% be sure that F is out. Is it because if T is out, the possibility of P-T is never possible, so F is negated? And same with if P is out, P-T is never possible, so we know F is out?

Please let me know if I need to clarify and thanks!