Re: Setup and Rule Diagrams

[Dave Killoran]

Setup and Rule Diagram Explanation

This is a Grouping Game: Balanced, Defined-Moving, Numerical Distribution, Identify the Possibilities.

Even though the bills appear to have a numerical order, it quickly becomes apparent that they can be paid in any order or configuration. More important are the groups of bills paid on the two days, and the key to the game is the Numerical Distribution of the bills to the days. There are seven bills that must be paid on Wednesday and Thursday, and the first rule establishes that three or four will be paid each day. This leads to two fixed distributions:

pt29_o99_g1_1a.png

These two fixed distributions suggest Identifying the Templates. We will initially set the game up that way and then discuss the decision to Identify the Possibilities. Let us begin by creating a basic diagram:

pt29_o99_g1_1.png

This game also contains a two-value system: all bills must be paid on Wednesday or Thursday. Since bill 1 and bill 5 cannot be paid on the same day, they must be paid on different days. But it is uncertain on which day each is paid, and so a 1/5 dual-option is placed on each day.

The two-value system also affects the last rule. The contrapositive of the last rule is:

pt29_o99_g1_2.png

Of course, if bill 7 is not paid on Thursday it must be paid on Wednesday, and if bill 6 is not paid on Wednesday, it must be paid on Thursday:

pt29_o99_g1_3.png

An examination of the final two rules suggests that the number of solutions is limited. Both rules contain bill 7, and especially important is the power of the 4-7 block. When the 4-7 block is applied to the 4-3 distribution, it has only one placement option; when the 4-7 is applied to the 3-4 distribution, it has only two placement options. On the basis of this limitation, a decision should be made to show all the possibilities of those three options. Each appears as follows:

pt29_o99_g1_4.png

Each of the three templates includes two possibilities, each dependent on the placement of bill 1 and bill 5. Overall the game has only six solutions. Let us examine each of the three templates in more detail:

• Possibilities #1 and #2: 3-4 Numerical Distribution. When the 4-7 block is placed on Wednesday, no other bills can be paid on Wednesday, and they must all be paid on Thursday. The only remaining uncertainty involves bill 1 and bill 5. Since there are only two options for bill 1 and bill 5, this template contains two solutions.
  
  Possibilities #3 and #4: 3-4 Numerical Distribution. When the 4-7 block is placed on Thursday, no other bills can be paid on Thursday, and they must all be paid on Wednesday. The only remaining uncertainty involves bill 1 and bill 5. Since there are only two options for bill 1 and bill 5, this template contains two solutions.
  
  Possibilities #5 and #6: 4-3 Numerical Distribution. The 4-7 block must be placed on Wednesday since there is only one open space on Thursday. When 7 is paid on Wednesday, it can be inferred from the contrapositive of the last rule that bill 6 is paid on Thursday. Since three bills are now paid on Thursday, bill 3 must be paid on Wednesday. The only remaining uncertainty involves bill 1 and bill 5. Because there are only two options for bill 1 and bill 5, this template contains two solutions.

Note that the use of templates to show two possibilities each reduces the amount of set up time required. The templates compactly display the uncertainty about bill 1 and bill 5, and there is no need to draw each of the six solutions out individually.

[Tommy2456]

Hello, I did this question and got all of the answers correct but what I did not understand is why is there a need to have three split game boards for this one? How do you know when more than 2 is needed? Also, if I would not have figured out that 3 was needed, could I have still answered the questions correctly with just 2 game boards?

[Emily Haney-Caron]

Hi Tommy,

Great question. The trick here is really making sure that your game boards together represent every possible solution to the game. In this case, it is easy to figure out you'll need a template for 3 on Wednesday, and a template for 4 on Wednesday. However, when I start to create those templates, I start to notice that it is difficult to represent all of the possibilities with just two game boards. That means that, if I want to identify the possibilities, rather than just the templates, I will need to have a third set. Identifying that is really about asking yourself how you need to set things up to represent every possible solution. Does that make sense?

Did you use only two boards for this question? If so, did you identify just the templates, or also the possibilities?

[jmramon]

Hi Powerscore,

I really had trouble interpreting rule #1 on this game after going over the answers. To my understanding, rule #1 meant that exactly 3 or 4 bills are paid on Wednesday, with the leftover bills paid on Thursday. However, the logic games bible says it's clear that rule #1 establishes that bills can only be paid on Wednesday and Thursday, which isn't stated anywhere in that rule that I can see. I was under the impression that since the stimulus says "on Tuesday an accountant has exactly seven bills to pay by Thursday," that Tuesday could be used as a bill-paying day too, which messed me up on question #3. I got all of the other questions right, however, in 7 mins w/o a template and by purely using hypotheticals. I'm frustrated because after rereading the rules several times, I see no mention that Tuesday is off limits as a bill-paying day. I feel like I'm losing my mind, can someone please explain where exactly this rule is stated or inferred? Thank you so much.

[Claire Horan]

Hi JMRamon,

Thanks for your question!

The rule states: "Either three or four of the seven bills must be paid on Wednesday, the rest on Thursday."

"The rest" means that any bills not paid on Wednesday are paid on Thursday.

Imagine if I said to you, "Give me three or four of the $7, the rest you can keep." You would certainly take that as a promise that you can have all of the remaining money, $3-4, not whatever was left over after I also gave some of the money to someone else that I hadn't mentioned.

Keep up the good work studying!

Claire

[jmramon]

Hi Claire,

Thanks for your help! I get what you saying, especially in terms of money. One more question though: why is Tuesday even mentioned then? Is it meant to try to throw test takers off? Or do I just have terrible language skills I always thought with logic games that if a course of action isn't explicitly prohibited, it could be a possibility.

[Francis O'Rourke]

Hi Ramon,

I can't say for sure if setting the scenario for this logic game on a Wednesday was meant to throw us off. I do know that it threw me off as well for a moment though! My original outline for this game has three groups, with the Tuesday group scratched out after I read the first rule.

You are right that whatever is not forbidden (or by common standards absurd) is possible in these games. The first rule however provides us with the prohibition against paying any bills on Tuesday. That is likely the biggest take-away from this game if you struggled with setting up the diagram.

As for the question of motivation, it may be possible that the test-makers wanted to make the game slightly more difficult and/or test our reading of the scenario and the first rule. It is also possible that the original test-maker thought that it was a realistic scenario to have an accountant sitting at her desk on Tuesday and plan out which bills to pay for the following two days. It is impossible to know the exact method behind this question, but it is clear that we were in effect being tested on understanding a slightly possibly tricky scenario.

[jmramon]

Ok, thank you very much for taking the time to respond! I'll study this one closer and try to be careful with the wording in the setups

[ValTitus]

I'm noticing an issue I seem to keep facing every now and then with game set-ups and I'm not sure how to resolve it. In this game in particular, I understood all of the rules and I applied the proper inferences and so-forth that the book reviews. But I misunderstood the prompt to include Tuesday in the distribution. So instead of having just a 3/4 or 4/3 distribution I had a 1/3/3 or a 1/4/2. I seem to have a similar issue with phrasing in other games and I would appreciate some guidance on how to better navigate those misunderstandings. In this case I understood that "On a Tuesday, an accountant has exactly seven bills... - to pay by the end of Thursday of the same week" to mean that the accountant basically has until Thursday to pay said bills. And since there wasn't anything explicitly stating that the accountant couldn't pay a bill on the Tuesday I assumed Tuesday should be included in the set.

[Rachael Wilkenfeld]

Hi ValTitus

It's really an issue of getting used to the precision in language the test makers use.

The first rule states that either 3 or 4 of the bills are paid on Wednesday, "the rest" on Thursday. That's a limitation like any other in the games. The scenario limits the possible days to Wednesday and Thursday by that language.

Imagine if you were going to a concert downtown with seven of your friends. Everyone meets up at your house, and there are seven cars available. If you said "I can take 3-4 people in my car, the rest need to go with John, you'd know the options were either your car or John's car. It wouldn't matter how many other cars were available, your statement limited things to just those two cars.

We have similar language here. There are different possible days to consider---Tuesday or even Friday if the bills end up being late. However that first rule limits the possible pay days to Wednesday and Thursday. It's either Wednesday or Thursday. That's what "the rest" has to mean there.

Hope that helps!