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The puzzle is as follows:

4 couples attended a magazine opening celebration party. These couples danced among themselves, all at the same time, to a disco suite, a pop ballad, a jazz tune and a waltz. Upon leaving the party the girls commented:

Natalie: I enjoyed dancing to a pop ballad with Rudy, then to a disco suite with Paul.

Patty: While I was dancing to a pop ballad with Danny, he kissed me.

Katherine: When I was dancing to a jazz tune with Tony, we bumped into each other.

Beatrice: I will never dance again to a jazz tune with Rudy.

Who danced to a waltz with Katherine and Beatrice?

The alternatives given in my book are as follows:

  1. Danny - Rudy
  2. Paul - Danny
  3. Paul - Rudy
  4. Danny - Paul
  5. Tony - Paul

I found this problem in my Reason and Logic book from 2000s under the topic of logical deduction. From its style it looks to be an adaptation from a reprinted copy of Martin Gardner's 70's book of Puzzle carnival.

My attempt to solve this problem relied on using a logic grid. Such approach seems problematic, as one sentence in the puzzle indicates that all danced among themselves, all at the same time which it makes it difficult to fill in a logic grid. Here if Beatrice dances the disco with Danny, that doesn't mean no one else can dance with Danny, or that no one else can dance the disco. This means it is more difficult to eliminate options.

Can this problem be solved using the logic grid approach? Please provide a picture driven explanation. This would be of much better help to me than just a set of statements, as in this peculiar situation I understanding a straightforward answer.

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  • $\begingroup$ I have edited to clean up some grammar, but I am still confused on this sentence: "A logic grid nulls an option as one is chosen to be necessarily true based on the fact that such choice does not repeat". In a normal logic grid, if one option is marked as true then you can mark all other options in the same row and column of that area as false. Is that what you mean? $\endgroup$
    – bobble
    Nov 16 '20 at 21:10
  • $\begingroup$ @bobble What I intended to say is that a logic grid applies to a set of a statements which are valid for one character of the story. Let's say is a set of A,B,C, then A is a baker, this means B is not a baker and C is also not a baker. Thus the baker condition applies for only one character in the story not to all or more than one. In this situation makes it difficult because all the musical pieces applies to all. Maybe the way how I attempted to tell this doubt was not expressed correctly? $\endgroup$ Nov 16 '20 at 21:26
  • $\begingroup$ I have attempted to edit your comment's explanation into the question. Please tell me if I worded it wrong. $\endgroup$
    – bobble
    Nov 16 '20 at 21:35
  • $\begingroup$ @bobble Thanks for doing that, yes that was what I intended to say. $\endgroup$ Nov 17 '20 at 12:37
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Interpretation:

"These couples danced among themselves, all at the same time, to a disco suite, a pop ballad, a jazz tune and a waltz". They all dance a to a (i.e. singular) disco suggest everyone dances 1 disco etc. They all dance at the same time then suggest each dance comes up once. They dance among themselves is less clear but suggests to me each boy/girl combination is used once. Allowing same pairs would mean no unique answer, as well as allowing boy/boy and girl/girl pairs. With this:

The answer is

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The grid

Danny Rudi Paul Tony
Natalie pop disco
Patty pop
Katherine jazz
Beatrice jazz

can be further filled in (easily in order 1,2,3,4) as

Danny Rudi Paul Tony
Natalie 2:jazz pop disco 3:waltz
Patty pop 4:waltz 1:jazz (disco)
Katherine 4:waltz (disco) 1:pop jazz
Beatrice (disco) jazz 3waltz 2:pop

More elaborate false/true format:

note: The standard logic grid approach does not work well because this puzzle connects 3 pieces of information in each statement, while the standard logic grid connects two. On can use a simplified but big 'logic grid' by combining 2 parts of the information e.g. dance pairs. Personally I prefer a tree dimensional approach (as sketched above) in this case.

enter image description here graph 1: fill in the 5 known dances (light green), those pairs do not do another dance (red), the female does not do the same dance (dark orange), and the males do not do the same dance (light orange). Natalie and Tony must be dancing a waltz (dark green).
graph 2: This new known dance prohibits Natalie and Tony to waltz with others. Natalie and Danny (as a pair) are left with only jazz, Patty and Tony are left with only the disco.
graph 3: This new known dances restricts Natalie, Danny, Patty and Tony further: thus leave Patty and Rudi with only the waltz, and Beatrice and Tony with pop.
graph 4: This new known dances leave Katherine and Rudi with only disco, and Beatrice and Paul with waltz.
graph 5,6,7 each step similarly restricts more , and fixes dances for pairs, until the complete solution is found in step 8

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  • $\begingroup$ It is an interesting approach but I still don't get why your grid is different from most of the grids which features a true-false similar to this? What sort of grid have you used?. Can it be translated into the example shown in the link?. Your solution seems condensed thus I'm not getting it how did you accomodated the conditions into the grid. Can you explain this more or put it in a split table?. Does it mean in this situation this approach is better? $\endgroup$ Nov 17 '20 at 12:33
  • $\begingroup$ I will really appreciate if you could include a step-by-step explanation of how did you concluded the rest maybe with a similar table as indicated in the link mentioned in the comment from above?. I'm really stuck in what criteria have you used to fill the rest of the table, can you help me with this part please?. $\endgroup$ Nov 17 '20 at 12:36
  • $\begingroup$ @ChrisSteinbeckBell Don't try to stick to the method you already know. Try to learn the various ways to model and approach a problem, and learn to pick the method that works best for a particular problem. Retudin's first method is arguably much easier to use than the "standard" true-false grid in this case: you can see that each row and column cannot have duplicates, which then can be solved like a 4x4 sudoku without boxes. $\endgroup$
    – Bubbler
    Nov 18 '20 at 1:41
  • $\begingroup$ @Bubbler Sure I also agree with what you say, my initial thoughts were confusion because I was not familiar with such kind of approach for a logic grid using names and not true false format, hence I requested an alternate version to compare which applies more efficiently in the problem. Because I'm still learning this was needed, as I am solving more of these by my own I'll feel familiar with such and the requests will not be needed. $\endgroup$ Nov 18 '20 at 20:04
  • $\begingroup$ @Retudin The source of my confusion was because I originally thought that all people dance all the musical genres with everyone in the sense that let's say Katherine would dance, disco, pop, jazz and waltz with the same guy and the next one and so on, which would make not applicable the logic grid. But it seems the intended meaning was that they would dance a musical genre with only person and not repetition and solely for this reason I believe that such disclaimer should be included in your answer because this helped me to understand the logic. Perhaps would you like to include this? $\endgroup$ Nov 18 '20 at 20:10

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