# Who took Gwen's purse and jacket?

The puzzle is as follows:

Four sisters went to the movie theater. While leaving the venue each one of them took by mistake the purse of another sister and the coat of another different sister. Maria took the coat that belongs to the sister whose purse Jenny took, while Jenny's coat was taken by the sister who took Maria's purse. If Gwen took Sophia's purse, who took Gwen's purse and coat respectively?

The alternatives given in my book are as follows:

1. Jenny and Sophia
2. Sophia and Jenny
3. Maria and Jenny
4. Jenny and Maria

The following puzzle comes from my Logic and Reason book from the 2000's and it appears to be an adaptation of a reprinted copy of Martin Gardner's book of the 1970s Puzzle Carnival under the section of logic grids.

I've attempted to follow a strategy but I became confused on how to arrange this information in a logic grid. Can this be done? The part which I'm struggling with is how to arrange these to match the condition of one people's taking another's belongings.

Can someone help me with this puzzle? Please include a step by step analysis because I'm lost on this one.

• In your question, you ask "I've attempted to follow a strategy but I became confused on how to arrange this information in a logic grid. Can this be done?". My understanding is that you are specifically asking for a logic grid, unless it is first proven this cannot be done. However, you didn't object to the graph answer offered by Bass. What are you asking for exactly? A logic grid? Any solution? And what qualifies as a valid logic grid? (i don't own any of those books of yours) Jan 1 '21 at 10:03
• Who is the author of this "Logic and Reason" book ? Aug 12 '21 at 9:19

This can be solved with a classic logic grid, with these three categories:

- Sister: Maria, Jenny, Gwen & Sophia
- Coat: Maria's, Jenny's, Gwen's & Sophia's
- Purse: Maria's, Jenny's, Gwen's & Sophia's

Here is the starting (empty) grid.

Step #1: let's fill it with the first information: "each one of them took by mistake the purse of another sister and the coat of another different sister"

Step #2: From "Maria took the coat that belongs to the sister whose purse Jenny took", you can infer that

Maria doesn't have Jenny's coat and Jenny doesn't have Maria's purse. Updated grid:

Step #3: From "Gwen took Sophia's purse", you can infer that

Sophia took Maria's purse, Maria took Jenny's purse and Jenny took Gwenn's purse. Those inferences are in gray in this updated grid (top-left square):

Step #4: From "Jenny's coat was taken by the sister who took Maria's purse", you can infer that

Jenny's coat was taken by Sophia.
It ensues that Maria took Gwenn's coat, Jenny took Sophia's coat and Gwenn took Maria's coat. These last inferences are in gray in this completed grid (bottom square):

So, "who took Gwen's purse and coat respectively?"

Jenny and Maria (4)

• Done, not instead but in addition to the online grids, so that anyone can play with them. Dec 30 '20 at 1:29
• @xhienne I'm having difficulties understanding. Because the categories are Sister's and girl's belongings. Are you referring in the top row Maria? or her sister?. Because in the second step you're crossing one girl's with the other girls belonging. This is some contradiction. I'm assuming that in the top row you're referring to the sister. Can you explain this better? Because the rest depends on it Dec 31 '20 at 21:27
• @xhiene Again the clue read Maria doesn't have Jenny's coat and Jenny doesn't have Maria's purse it doesn't say Maria's sister neither Jenny's sister, and in the top row categories you define those to be their sisters, not the girls. This seems a contradiction, can you explain this better please?. I'm stuck. Dec 31 '20 at 21:29
• @ChrisSteinbeckBell First of all, those are screenshots of the webpage I linked to. The first 4 top rows (the forenames) are fields to be defined and do not belong to the logic grid; ignore them and you get the 2x2 logic grid you asked for (didn't you?). As for whom I'm referring to with a forename, I don't understand your question: I'm referring to the girl with that name. They are all girls, they are all sisters, each girl is identified by her name. If I'm crossing one girl's with the other girls belonging, that means the former didn't take the latter's belonging. Jan 1 '21 at 9:46

For some reason (I have no idea why) this puzzle is screaming "Graphs!" at me.

So let's do graphs. Here's the basic situation:

Put in the given clues:

Connect the two-coloured blobs to the only persons that still have both colours available:

And oh look, we are already done!

• Interestingly, it turns out the Hugely Important sounding negative constraint of "nobody got their own coat or their own purse" is a complete and utter red herring! Anything we can deduce, we can deduce without it. (See above.) Speaking of everything we can deduce, Maria obviously got Jenny's purse (there's only one unconnected red dot on either side), but we'll need to use the "everyone got a coat that is from a different sister than the jacket they got" constraint to place Maria's coat on Gwen and finally Sophia's coat on Jenny.
– Bass
Dec 30 '20 at 17:22
• I'm stuck at understanding your solution. What do the blue and red dots mean?. Do they mean coat and purse? Why do both names appear on the left and on the right?. The blue words imply taking coat and the red words imply taking purse but I think this is for the lines. Anyways I'm stuck at the lines connecting Jenny and Maria both on the left and right, these are black, what do they represent for each side? Why is this joined by a blue dot?. What does it mean?. I find this confusing. Dec 31 '20 at 21:39
• The red dot on Gwen on the left is connected by a black line to the blue dot on Sophia on the right. Why?. What's the meaning of this? Both Sophia red and blue dots on the left are connected by a yellow line on the left to the blue dot of the intersection between Maria and Jenny on the right. Why? The same from Gwen with both blue and red dots on the right with a yellow line connected to the intersection between Maria and Jenny on the left. Why?. This I don't understand. Why are these connected by a yellow line? Why not the others?. Dec 31 '20 at 21:43
• I think you can figure all of these out if you stop for a moment, and look at the first picture (without the clues) for a moment. The basic idea is to connect same coloured dots to make sentences, The colour of the lines has no meaning except for telling the lines apart, the colours of the endpoints determine the meaning.
– Bass
Jan 1 '21 at 1:39

I did it a little bit differently.

1. First I rewrote the information into personalized fact statements:
• Jenny took X's purse, Maria took same girl's coat.
• X = Gwen or Sophia
• Either Gwen or Sophia took Jenny's coat AND Maria's purse.
• BUT Gwen took Sophia's purse
1. Then I filled in a simple table of who has taken whose what:
Maria Jenny Gwen Sophia
Maria has taken
Jenny has taken
Gwen has taken Purse
Sophia has taken

We know Gwen took Sophia's purse

1. Since Gwen took Sophia's purse, she cannot be the girl who took Jenny's coat AND Maria's purse. Thus we get:
Maria Jenny Gwen Sophia
Maria has taken
Jenny has taken
Gwen has taken Purse
Sophia has taken Purse Coat

Sophia took Jenny's coat AND Maria's purse

1. Since Jenny has not taken her own purse, we can now see she must have taken Gwen's purse.
Maria Jenny Gwen Sophia
Maria has taken
Jenny has taken Purse
Gwen has taken Purse
Sophia has taken Purse Coat

5. This shows us Gwen is the mysterious X from our first fact, thus Maria has taken Gwen's Coat! Problem solved. Gwen's purse and coat were respectively taken by Jenny and Maria.

|                  | Maria | Jenny | Gwen | Sophia ||------------------|-------|-------|------|--------|| Maria has taken  |       |       | Coat |        || Jenny has taken  |       |       | Purse|        || Gwen has taken   |       |       |      | Purse  || Sophia has taken | Purse | Coat  |      |        |

• I'm wondering about the other posibilites not listed in your table. Jenny could have taken Maria's coat or Sophia's coat. Isn't it?. Maria could have taken Jenny's purse or Sophia's coat?. Can your table be filled with the given information or is it not possible to deduce these unknowns?. Can you help me with this? Dec 31 '20 at 22:28
• From my little table we can further deduce, that Maria has taken Jenny's purse. It is the only one left for her. We can also see Gwen must have taken Maria's coat (since only Maria's and Sophia's are available, and she has already taken Sophia's purse [and we've been told no one has taken coat AND purse of same sister]. And last piece of info is then that Jenny has taken Sophia's coat, since it's the only one now left. Jan 4 '21 at 7:45