Setup and Rule Diagrams

[reop6780]

Thanks for answering somewhat obvious question that I had!

[Dave Killoran]

Glad to help, and it wasn't obvious at all

Thanks!

[sonnenstrahl]

Here goes my first post...

The prompt is the following "Three boys - Karl, Luis, & Miguel - and three girls - Rita, Sarah, & Tura - are giving a dance recital...." [Admin note: Full text of question removed due to LSAC copyright restrictions]

I did not have a problem with the questions of the game, but with the underlying assumption of its set-up: that every girl and every boy performed the three dances.

When I initially set-up the question, I created the following diagram...

___R ___R ___R
___S ___S ___S
___T ___T ___T

But then, I started erasing, thinking that I had to be more open-minded... why did I assume that every girl performed each dance? Even though no two duos would be repeated (per rule 3), could not a girl or boy be repeated in the same dance?

I understand that if the dancing partners were dancing -simultaneously- that physically Sarah cannot dance twice in Dance 1. But why is that option precluded from occurring, if the nature of the routine isn't specified?

Thank you in advance for any advice that is offered!

[Jon Denning]

Hey sonnenstrahl,

Thanks for the question, and welcome to the Forum!

I think here we can presume that, because of the real-world nature of how dances occur and because we're told "each dance involves three sets of children," we can know that, say, dance 1 involves all six at once with three simultaneous pairs. That means that for each dance all three boys and all three girls are partnered with one another, and no boy could dance with two girls while someone else is left out.

What's encouraging here is that you're looking to test the limits of what could occur, and that's a key idea for a number of games. Just don't go beyond the reality of a situation that has physical implications (in the same way that someone visiting cities couldn't be in two different places at once).

I hope that helps!

[sonnenstrahl]

Hi Jon,

Thank you for your response! Much appreciated.

[kristinaroz93]

This was a tough game !
I am actually trying to understand the rules still:

1) a) "No two children can partner eachother in more than one dance". Does that mean for instance, you cant have l+r and l+r both dance together in dance 1 and then dance 2, in addition to the fact that that no child can dance more than once in any given dance generally (i.e. if l already danced with someone in dance 1,I cannot dance in dance 1 again even if with a different partner)?
b) And How did we automatically know that 3 pairs meant 6 DIFFERENT people in total for each dance and not having any repition at all!!? Even though this repeats the last point, can't someone go again in dance 1 but just with a different partner this time?Why can there be no repetition going vertically of male dancers as the diagrams presented in the bible explanation section show (starts pg 420 of games bible)?

(Maybe this is very obvious but I still don't see it very well)

2) And I also don't get (probably becuse the rules have confused me) how we have reached the inferences of "one boy must partner with t in dance 1, r in dance 2, and s in dance 3. One boy must partner with r in dance 1, s in dance 2, and t in dance 3. One boy must partner with s in dance 1, in dance 2, and r in dance 3".
Would anyone be so kind as to help me with this problem=) Thanks in advance!

[Ladan Soleimani]

Hi Kristin,

This is definitely a difficult game with some complex inferences.
1) You are right about the first part of this. The rule means that you cannot have the same pairs repeat. So if Rita dances with Karl in dance one, then she cannot dance with him in dance two or three. As for how we know that each child only dances once per dance, the scenario tells us that there are 3 dances and "each dance involves three pairs of children, a boy and a girl partnering each other in each pair". There is no indication that a child can switch partners in the middle of dance. So during dance 1, there will be three pairs dancing at the same time so they have to be 6 different people. There is no linear element within Dance 1; it is not as if one pair will dance, then another pair, and then the third pair.

2) Those inferences come from a combination of all three rules. The second rule states that the same person who dances with R in dance 2 dances with S in dance 3. Since pairs cannot repeat, the third rule, that means that the person who is with R in 2 and S in 3 must be with T in 1. We also know that this person is not K because the first rule tells us K is with S in one or 2, not dance 3. That is the easiest of those inferences. Then look at the first rule: K partners S in either dance 1 or dance 2.

If K is with S in dance 1 several things must happen. In dance two K cannot be with S again and we know that it cannot be paired with R, because again the same person paired with R in two must be paired with S in three and K cannot be with S in three since we are pairing it with S in 1. So K has to be with T in dance 2. Then in dance three K must be with R because that's the only girl he hasn't paired with. So K will be with S in 1, T in 2, and R in three. From the first inference above one person is with T in 1, R in 2, and S in 3. So the only spots left for the third boy are with R in 1, S in 2, and T in 3. The same pattern emerges if you place K with S in dance 2. One boy must partner with T in dance 1, R in dance 2, and S in dance 3. One boy must partner with R in dance 1, S in dance 2, and T in dance 3. One boy must partner with S in dance 1, T in dance 2, and R in dance 3. The easiest way to see these may be to draw out hypotheticals.

When writing out the hypothetical to see the pattern, start with K with S in 1 or 2 and then just pick either L or M as the person with R in 2 and S in 3 instead of writing them as dual options. So writing out K with S in 1 and picking L as the person in the second rule who is with R in 2 and S in 3 would start like this:

R __ L __
S K __ L
T __ __ __

Since L is paired with R in 2 and S in 3 then it has to be with T in 1 so there are no repeats (that first inference)

R __ L __
S K __ L
T L __ __

In dance 2, K cannot be with S again so it has to be with T. In dance 3 K must be with R since it has been with S and T.
R __ L K
S K __ L
T L K __

The only spots left for M are R in 1, S in 2, and T in 3

R M L K
S K M L
T L K M

Again, placing K with S in 2 gives the same pattern. I hope this helps you understand where the inferences come from.
Ladan

[wickedcat]

Hello PS crew,

I have the exact same inquiry but still cannot wrap my head around why each boy and girl need to do each dance. Depending on what type of dance, but if a boy - say Karl - dances with Rita, Sarah and Tura for dance one, doesn't that also constitute three pairs of children, in which case neither Luis and Miguel are dancing? Please help!

*Edit: Essentially my question is why should I assume that each child-pair is dancing simultaneously in the one dance?

[Emily Haney-Caron]

Hi wickedcat,

Thanks for the question! This is definitely a really tricky one. It might help for me to pull out for you the sentence in Ladan's reply that answers your question:
"There is no indication that a child can switch partners in the middle of dance. So during dance 1, there will be three pairs dancing at the same time so they have to be 6 different people."
Basically, it is implied that the pairs are all dancing at once; that means that all 6 children will have to be involved in each dance. I hope that helps!

[akalsi]

Hi,

I did this game as part of the homework section. After reading the explanation I'm unsure if i approached this game correctly. I basically used my knowledge of the game and made 4 templates where in two of them K was with S in dance 1 and either L or M was in dance two and three for R and S respectively, and two similar templates where K was with S in dance 2, and did the same approach with L and M. I ultimately was able to come up with 4 complete templates after filling in the blanks, and used those templates to attack the questions, and I'm happy to say I did answer all the questions correctly.

Was the approach I used appropriate in this game - i.e. making 4 (ultimately completed) templates? (I guess I'm just looking for reassurance that I understand how pattern games work! )