The Dishes Problem

Solution:
The dishes problem was a bit easier than I initially thought it would be. After rereading the problem and taking a few moments to think about it, I came to the conclusion that the number of guests must be a common multiple of 2, 3 and 4. I then started listing out the multiples for each and made another list containing the common multiples.

Common Multiples: 12, 24, 36, 48, 60

Using this list, I added the divisors to see if they would add up to 65. After a few tries, I found that 60 was the magic number.

(60/2) + (60/3) + (60/4) = 30 + 20 + 15 = 65

Therefore, there were 60 guests at this dinner.

Whether it makes a difference to our students to offer examples, puzzles and histories of mathematics from diverse cultures (or from 'their' cultures!)
I think the selection of puzzles and histories does make a difference to our students. By showing students that math was done by all kinds of civilizations during all time periods and all cultures will help to broaden their minds that math is not just for old white men. I do not want to discredit what these men discovered, but I would like the students to see that they were not the only ones coming up with amazing math. For me, I always became much more interested in a topic/subject when I discovered that there were ties to my culture. I felt like I could relate to it better and I had a deep sense of pride knowing the people of my culture were able to do such wonderful things. At the same time, I was liked to learn from diverse cultures too. Many times I was surprised at how similar they are to mine at time while also learning about the differences. 

Whether the word problem/ puzzle story matters or makes a difference to our enjoyment of solving it?
The context/story make a large difference to me when solving a problem. One of the issues I had with this problem was the context. It made absolutely no sense to me how the official and the cook did not know the number of guests. Did the official not sign off on the guest list? How was the cook able to prepare enough food without knowing the number of people eating? I also wanted to know what type of gathering this was. Was it a celebration, and if so what were the people celebrating? What was life like in 4th century CE China? Knowing more about the story of the problem would have made it more enjoyable for me because I would be able to think of each of the 60 people in this problem as a real person who lived in China during the 4th century rather than just an answer to puzzle.