Setup and Rule Diagrams

[Jeremy Press]

Global Diagram:

1. The scenario presents a balanced, advanced linear setup, where 2 floors (of a building's floors from 1 to 8) must be examined each day from Wednesday through Saturday, and each floor must be examined exactly once.

2. The first rule is the most difficult to represent visually. It would be better to write out what it means in the rule list and apply it once you have determined the placement of one or more of the variables. The rule means that on any given day, two floor numbers that are consecutive cannot both be examined (e.g. 1 and 2 cannot be examined on the same day, 2 and 3 cannot be examined on the same day, etc.).

3. The second rule is a sequencing rule placing floor 2 on an earlier day than floor 8, with resulting not-laws showing that floor 8 cannot be examined on Wednesday, and floor 2 cannot be examined on Saturday.

4. The third and fourth rules combine into a chain sequence rule, in which floor 3 is examined on an earlier day than floor 7, which is examined on an earlier day than floor 5. The resulting not laws are that floor 3 cannot be examined on Friday or Saturday, floor 7 cannot be examined on Wednesday or Saturday, and floor 5 cannot be examined on Wednesday or Thursday. This rule can be used as the basis for four templates, per below.

5. The final rule places floor 4's examination on either Thursday or Friday.

6. Floors 1 and 6 are random variables.

The global diagram representing each of these rules is below:

Global Diagram - Game 4 December 2017.png

Template 1: Floor 3 on Wednesday, Floor 7 on Thursday, Floor 5 on Friday

1. In this template, floor 4 must be examined on Thursday, since it cannot be examined on Wednesday or Saturday, and since it cannot be examined on the same day as floor 5, with which it is consecutive.

2. Floor 2 cannot be examined on Wednesday, since it cannot be examined on the same day as floor 3, with which it is consecutive. That means floor 2 must be examined on Friday, the next open day, since it cannot be examined on Saturday. That means floor 8 must be examined on Saturday.

3. Floors 1 and 6 are dual options on Wednesday and Saturday.

Template 1 diagram:

Template 1 Game 4 December 2017.png

Template 2: Floor 3 on Wednesday, Floor 7 on Thursday, Floor 5 on Saturday

1. This template is more open-ended, since floor 4 can be examined on either Thursday or Friday.

2. For time purposes, the split implied in this template need not be pursued further, although it's worth noting that (just as in Template 1) if floor 4 is examined on Thursday, floors 2 and 8 will have to be examined on Friday and Saturday respectively.

3. Floor 1 or floor 6 must be examined on Wednesday with floor 3, since floor 2 cannot be examined on the same day as floor 3 and floor 8 cannot be examined on Wednesday.

Template 2 diagram:

Template 2 Game 4 December 2017.png

Template 3: Floor 3 on Wednesday, Floor 7 on Friday, Floor 5 on Saturday

1. This template is more open-ended, since floor 4 can be examined on either Thursday or Friday.

2. For time purposes, the split implied in this template need not be pursued further, although it's worth noting that if floor 4 is examined with floor 7 on Friday, floors 2 and 8 will have to be examined on Thursday and Saturday respectively.

3. Floor 1 or floor 6 must be examined on Wednesday with floor 3, since floor 2 cannot be examined on the same day as floor 3 and floor 8 cannot be examined on Wednesday.

Template 3 diagram:

Template 3 Game 4 December 2017.png

Template 4: Floor 3 on Thursday, Floor 7 on Friday, Floor 5 on Saturday

1. This template is more restricted, because floor 4 cannot be examined with floor 3 (with which it is consecutive) on Thursday, and therefore must be examined on Friday.

2. Since floor 2 cannot be examined with floor 3 on Thursday, and can never be examined on Saturday, it must be examined on Wednesday.

3. Since floor 1 cannot be examined with floor 2 on Wednesday, floor 6 must be examined on Wednesday.

4. Floors 1 and 8 are dual options to be examined on Thursday or Saturday.

Template 4 diagram:

Template 4 Game 4 December 2017.png

The templates reveal an interesting further inference that one of floor 1 or floor 6 is always examined on Wednesday.

I hope this helps!

Jeremy

[alisonroberts29]

Could you explain the set up of this game, specifically the inferences you can identify? I was able to note a lot about which floors could not be examined on which day, but that still didn't seem like enough to get through the questions quickly. Thank you!

[Robert Carroll]

Could you explain the set up of this game, specifically the inferences you can identify? I was able to note a lot about which floors could not be examined on which day, but that still didn't seem like enough to get through the questions quickly. Thank you!

Alison,

It sounds like you are on the right track. You should set up the days of the week as the base and infer Not-Laws from the various rules. The third and fourth rules will be especially helpful, as they combine as follows:

3 7 5

Each element in this sequencing chain will be prevented from being on two separate days:

Floor 3 is excluded from Friday and Saturday

Floor 7 is excluded from Wednesday and Saturday

Floor 5 is excluded from Wednesday and Thursday

This already allows you to infer Split Dual Options for each of these variables, as each is now restricted to only two places.

Remember, though, that the game also gives you another variable restricted to two places - Floor 4 (last rule). What you'll find is that Floor 4's options (Thursday and Friday) coincide with some of the options for Floors 3 and 5. The very first rule in the game will prevent 4 from being on the same day as 3 or 5, so, while there's no further inference beyond the Split Dual Options for 3, 4, 5, and 7, it's relatively easy for 4 to find itself unable to be examined on a day because of the presence of 3 or 5 on that day. This isn't quite a Global inference, but it takes so little additional information to make happen that it will easily come up in specific questions, either because of Local conditions in the question or because of aspects of the answer choices that force 3, 4, or 5 into certain days.

Robert Carroll

[Jeremy Press]

Hi,

Above I've posted a global diagram (with a few comments), and the 4 templates (with a few more comments) within which the 3-7-5 sequence can be placed.

Thanks!

[gwlsathelp]

For me, this was incredibly hard to identify the templates, would it have been better to have just gone to the questions with the global templates?

[gwlsathelp]

Wait a second, a couple more minutes thinking about how to approach identifying the templates and I had a breakthrough. This all hinges on the most restricting rule 3 — 7 — 5. I distributed it out and turns out there are only four ways to do so, just like above, and I more or less got the same thing.

[dimi.wassef@yahoo.com]

I still can't seem to wrap my head around the idea of Numerical distributions in terms of a ratio, and how to spot template opportunities. Also, for this game, are inferences required to answer the first question? I could not seem to answer the question just by looking at the rules.

Thanks!

[Robert Carroll]

dimi.wassef,

Templates are a big topic and I'd suggest looking at each game explanation thread with templates for an idea of what features of the game encouraged a PowerScore instructor to do templates. In this game, there are only a few ways to fit the 3 7 5 chain into the four days, and each way to do that leads to some further template-specific inferences, like the placements of 2, 4, and 8. So: there are only a few places to put the elements of the sequencing chain, and at least a few of those limited placements seem to have further consequences for other variables. Few options + extra template-specific consequences = templates are a good idea.

The first question is a Partial List question - in fact the rules alone should answer the question, but it can take more work to see that because of the necessity of "filling in" the details of the days not mentioned in each answer. So: eliminate answers that are wrong on their face and, for the remaining answers, consider whether they cause a problem on the unmentioned days. Eliminate those that do until only one answer remains.

Robert Carroll