Setup and Rule Diagrams

[Administrator]

Please post your questions below! Thanks!

[Marathon]

Hello,

Can you please post the proper set up and inferences for this game? It took me longer than expected to complete and I feel as if I missed something. Thanks.

[James Finch]

Hi Marathon,

This is a classic template game, as we're given a couple of either/or rules. This means we should be prepared to create 4 templates for this game, although one or more may not actually be possible and follow all the rules.

Variables: GHRST
Rules:
1) H--R
2) G-T H--R--T and S--T (T must go last in this scenario)
Contrapositive:
T--R or T--S T--G
3) H--S and T and R
or
S and T--H--R

So the scenarios I would create would be:

1) H--R and S--T, G--T
2) H--S and T and R, T--G, T--R or S or both (this is the trickiest one)
3) S and T--H--R, T--G
4) Doesn't work, as it forces both G--T--R, which isn't possible according to the rules

Using the first 3 templates, (ideally drawn out rather than written out the way it is here) we can quickly answer all of the questions accurately.

Hope this helps!

[sophiaT]

Hi,

Do you know of any of other games where there is a rule that is conditional and the necessary includes a chain.
I mistakenly thought the contra postive was T-G T-R,S and therefore, simplified, the contra postive could be read T-R,S,G

Thank you!

[Adam Tyson]

There are plenty of them out there, sophiaT, and if you have access to our course books of the LG Bible you will find some in the lessons and chapters that deal with Pure Sequencing games, and they also show up in Basic Linear games. Here are a few that I found:

June 2016, PT 78, Game 3
December 2011, PT 65, Game 4
June 2010, PT 60, Game 2

Check these out, and consider three possibilities every time you encounter one of these rules:

1) The sufficient condition happens, and the necessary happens
2) the necessary condition does not happen, and the sufficient condition does not happen
3) the sufficient condition does not happen, and the necessary condition does happen

That might mean three diagrams, but if that's the best approach then it will turn out to be worth the time and effort!

[sophiaT]

Thank you!

[180bound]

Hi, using the templates suggested here really helped.

My question is what about this game on the outset made you think templates? Could you break down your decision to use templates and could you break down how/why you combined the rules in the way you did? Once I used your method the game was extremely easy; however, I can’t seem to push through as seamlessly when I do it without assistance as I have hard time reproducing your templates. I read the bibles and listen to the podcast about template games and I’m so used to looking for I guess “simpler” rules that suggest using templates i.e. “S can only go in spots 3 and 4”.

Thanks!

[Robert Carroll]

180,

Essentially any Pure Sequencing game with conditional rules or "either/or/not both" rules can profitably be attacked using templates. An "either/or/not both" rule creates two possibilities, and a conditional creates three, so, in theory, a game with one rule of each kind will have six templates. In actual practice, it usually happens that some of the combinations don't work, which is good, because it reduces the list of templates. As Adam pointed out, June 2016, PT 78, Game 3 is an excellent example of this kind of game.

Robert Carroll

[missalyssacarr]

Hi ,

I had some trouble with this question and did not see the opportunity to use templates. Could you please explain each of the templates you identified?

Thanks,

Alyssa

[Luke Haqq]

HI Alyssa,

I can expand a bit on the thorough explanation provided by James above. He notes three possible templates

1) H--R and S--T, G--T

This follows from the second rule. This template supposes that G comes before T. When that is the case, the rule tells us that "Roberto and Sonja must also perform earlier than Toshiro." Whenever G--T, we know from this rule that T must occur last, because H, R, G, and S all must occur before it.

2) H--S and T and R, T--G, T--R or S or both (this is the trickiest one)

This template acts as if it were not the case that G--T; that is, is supposes that T--G. This template also supposes that H--S and T (which is one of the two options from the third rule. If T--G, then we know from the second rule (from its contrapositive) that one of three possibilities is also the case: (1) S--T--G, (2) R--T--G, or (3) S and R--T--G. We also know from the third and first rules that either (1) H--S and T and R, or else (2) S and T--H--R.

3) S and T--H--R, T--G

This again supposes that T--G. However, instead of supposing H--S and T (one of the two options in the third rule), this template places both S and T before H, or "S and T--H." Since we know that H--R from the first rule, we can plug this in as well, so this latter possibility more completely would be S and T--H--R. We also know that T--G in this template, though we don't know precisely when after T that G will occur (it might come before, after, or in between H and R).