The Dishes Puzzle problem

The way I approached the problem was by finding a lower limit and upper limit for the number of guests. Given that we have 65 dishes, the situation where there are least amount of guests will have be that everyone is eating rice only, so 65*2 = 130 guests. And the max number of guest will be that everyone is eating meat, so 65*4 = 260 guests. With a range, we can test out each number. And see if when being divided by 2,3,4, the sum of the dividends will add up to 65. 

Offering students a historical background in mathematics not only supplements their learning but also deepens their appreciation for the subject's vast diversity. By understanding the origins of mathematical concepts, students can see how different cultures across the world contributed to its development, from ancient Egypt and Mesopotamia to China, India, and the Islamic Golden Age. This awareness helps them recognize that math is not a static or isolated subject but a universal language shaped by human experience across time and geography. It opens up perspectives, allowing students to embrace other cultures and recognize the global impact of mathematical discovery.

Additionally, incorporating puzzles and imagery into word problems makes the scenarios feel more grounded and authentic. This approach reminds students that mathematics is not just an abstract concept confined to the classroom but something rooted in everyday life. When students are searching for solutions, it helps to see math as a reflection of real-world situations and challenges. By grounding problems in reality, we emphasize that mathematical thinking stems from the natural world and human experiences. This connection not only enhances problem-solving skills but also adds meaning to the task, making it more engaging and relevant. Ultimately, this approach brings math to life and fosters a deeper understanding of its practical applications.

Solution to Puzzle Problem

In tackling this problem, I was able to determine that 1 and 3 must be among the four weights, while the other two weights fall between 10 and 30. However, because I was using an elimination-by-exhaustion approach, I didn’t explore all the possible combinations. For a one-pan scale, the five weights would be 1, 2, 3, 6, and 21.

This puzzle can serve as an introduction to combinatorics, demonstrating how different combinations can be assembled to achieve a desired outcome. Students can explore how many possible combinations exist, which work, and which don't. This encourages them to practice elimination and grouping methods, while strengthening their understanding of numerical expressions and the concept of equality.

The puzzle also ties into number theory, illustrating how numbers can be manipulated in various ways. I started to imagine possibilities beyond one- or two-pan scales. Could there be three, four, or even more pans for measuring a larger number of weights? I believe there could be a pattern that forms an arithmetic series.