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Finding the 880 4x4 Magic squares

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Tags: magic-squares-investigation-complexity-discrete-maths-boolean-algebra

The magic square is an ancient puzzle that is not fully understood today. The 3x3 has only one solution but the 4x4 has 880. I was very surprised to discover how difficult the 4x4 magic square is and I conducted an investigation to find all the solutions. This style of Maths investigation can be useful for everyone. I wanted to demonstrate how I handle a problem when I don't know which maths techniques are involved. I tried to make the video as colourful as possible. This actually was how I solved the problem on paper first by thinking about coloured grids and I tried to represent that on screen as a demonstration in problem solving rather than displaying maths that I already understood.. Although the problem is connected to very difficult computer science theory I kept this video completely algebra free so it can be watched by high school and even younger students. However the ideas of Boolean algebra and computational complexity are related to degree courses. I

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3.49 Overall score*

163 Rank

8 Votes

5 Comments

Comments

5.2

The starting position is a very clear and intuitive problem. However, I think including Pseudo-code to explain the algorithm you used for finding the squares would have been useful for understanding what exactly you did. Showing the 880 possible squares at the end again made it very clear what your final result is.

4.9

This felt more like a vlog than a structured video on the topic.

Edit: Lurking in the SoME discord, saw your comment on my review. Fair call-out! On reflection, I agree I don’t think I graded it fairly initially. I was viewing it more as “explain this topic” video rather than “here’s my journey on this topic”.

With that in mind, I enjoyed the video much more the second time around. I still think it could do with some more structure. It seems like you’re talking off of notes/memory rather than a script, but I do appreciate the more off-the-cuff casual feel you give.

2.3

There are a couple of editing errors and the video could use some more polish overall. It feels like more of a discussion of a recreational math exploration than a math explainer. Some of the terminology is also used incorrectly (e.g., I think you meant to use “brute force” or “exhaustive search” instead of “dictionary attack”).

I liked the exploratory approach, that you were trying to show how you approach a problem, with all its warts, rather than just giving us the answer.

3.5

I think it would have made sense to give the definitions of the different kinds of magic squares at the start and with clear visualisation. I still don’t know of which kind of magic square there are 880 of (i.e, does that include diagonal constraints and how many) and I don’t know what you referred to when you mentioned the perfect square requires the “third diagonals”, so getting these clarifications out of the way would have helped. You already had the system set up to show the cumulative sums per row, so only showing the sums for constraints under consideration might have done the trick. The same goes for the symmetry considerations: Visualising the translations etc. would have made it clearer why, when and which you need to consider.