If Sarah partners Luis in dance 3, which one of the following is a complete and accurate list of the girls any one of...

Ravi on February 9, 2022

For this setup, it's best to split the game board up with the rule about K having to partner with Sarah in dance 1 or 2.

With the first board, K partners with Sarah in 1, and the second board, K partners with Sarah in 2.

Then, look at the other rules. With rule 2, we know that whoever partners with Rita in 2 has to partner with Sarah in 3. We also know that this person has to partner with Tura in 1 because rule 3 tells us no two children partner for more than one dance.

Knowing this, the last boy has to partner with R in 1. For 2, we only have S and T open, so K has to partner with T in 2, and the last boy will partner with S in 2. For 3, K must partner with R since he hasn't yet, leaving the last boy to partner with T in 3.

With the second board, K is with R in 1. Since whoever's with R in 2 is with S in 3, we know that person is with T in 1. The remaining boy will partner with S in 1. In dance 2, that same boy will have to partner with T in 2, so K will be with S in 2. Then, for dance 3, we know that the remaining boy will be with R in 3 and then K will be with T in 3.

For this question, if L and S are together in dance 3, then L and R have to be together for dance 2. And, since L is with S in 3 and R in 2, then L has to be with T in 1 because he has to have a new partner for every dance. From this, we know the remaining partners for Miguel in dance 1 are R and S, so D is the correct answer.