Summer of Math Exposition

While I enjoyed the video and appreciated the unique style, I feel like the pacing is too fast as it glosses over new group theory concepts that would likely be foreign to a high schooler. The motivation is nice, looking at a puzzle and verifying a statement it makes. Overall I did like the video, but my main issue is that new group theory concepts get explained too fast.

I liked the format and your choice of using a game as the motivation The music was distracting at times, just lower the volume a bit when you’re talking Some jargon was not explained, like the choose formula and the ∈ symbol Overall, nice high quality video. Great job!

It has some nice high school maths moments, but as its label says goes beyond school maths into group theory which is quite challenging. I like the game and the fun moments about the name and the result, but won’t be able to use it in school.

Very nice production! Original topic. Thank you!

Thoroughly enjoyed this! Even though at least half of it went over my head, I was entertained throughout and I did get some insights from it. Everything about the video feels totally pro: pacing, narration, sound quality, colouring - this is polished to a very high standard and right up there with the best youtube content. I particularly liked the music, it’s great to hear something that sounds like a real performance on a real piano, rather than the ubiquitous sample-based ambient tingle tangle - I wish 3B1B would take a page from your book in that regard :) The only thing I didn’t really like was the final sentence, it was kind of funny but it felt like a bit too much of a mic drop to me.

Nice animation and very clear narration.

This is a fun and enjoyable video, and at the same time it nicely illustrates the idea of how symmetries can be used to reduce the complexity of combinatorics calculations.

I think it would be pretty much impossible to follow all the details in real time, but perhaps you weren’t expecting viewers to do so? Also, under “Audience” it says “high-school” - was that deliberate? The video assumes a lot of terminology that a high-schooler wouldn’t know (e.g. I think you used the terms “bijection” and “equivalence class” without definition). But perhaps your intention was that even if viewers (including high-schoolers and probably also pretty much all other viewers) wouldn’t manage to understand the details, still seeing the full solution worked through and visualised is engaging and inspiring, and might instil a fascination with group theory even in viewers who did not follow any of the group-theory details?

I would say you sometimes subconciously use technical terms you haven’t defined! A highschool student might not understand them. This is fine if it’s just a little bit of added technical detail for people who know the stuff, but i think it goes a bit too far in this case! The music is slightly too loud!

Other than that very cool video!

This is an excellent exposition on combinatorics and group theory, and the ideas used in the video are very well-motivated and covered in great depth. The video stands out because it takes the seemingly simple concept of counting permutations on a Color Cube Sudoku and using mathematical rigour to debunk its packaging claims. It also serves as a great case study in mathematical verification and critical thinking, and gives a fun outlook on recreational mathematics. That said, I wouldn’t expect any less from Joseph Newton since his videos are consistently brilliant.

You kinda lost me a bit towards the end because I couldn’t keep all numbers in my head. But otherwise a very nice exploration of this puzzle!

I really like the idea of the video. I can see this being a fun introduction to group theory or combinatorics, but the execution was extremely off.

I think it could work for people who already understand group theory, but the audience being marked as high schoolers really through me off. If you were to target a higher audience though, the format would still have to change to reflect that.

The notation, language, and such was introduced VERY rapidly and there was a lot to digest. I’m not sure how you expect to teach someone what a permutation is and an “orbit stabilizer theorem” in the same video.

I even have some background on set theory and combinatorics and I was incredibly lost.

I would’ve liked to see other visuals in the camera parts that help explain what you’re talking about and to keep track of ideas. Also, in the more math and notation parts, I would’ve liked to see better visuals and explanations.

The whole video felt like someone reading a textbook chapter rather than an explanation for lecture or video format. This was especially jarring with the game hook. If it were an “intro to group theory” that would be different, but even then it’s so poorly paced.

Also, there was no explanation of how the game worked until a few minutes in. By the time you explained it, I was already lost.

Loved it! I wouldn’t haave minded a link to a good intro on group theory (including group actions).

Good video. I feel like there is a bit of the experts familiarity here as I got a little lost in the group theory section.

very charismatic. and understandable without knowing group theory and tickled the right place in my brain

“So this game isn’t about colours, or cubes, or sudoku.” — Voltaire, 1761. (I wonder how many SoME viewers would recognize that reference.)

Pretty good. the facts are explained pretty well, a fun showcase of Group Theory, pretty heavy substance, so could give the viewer some room to breathe.

Really well made video on a topic and a game I never knew about! this was such an informative video. the motivation was clear from the start, the goal was clear from the start as well. Clarity was extremey good, although at some places I felt like I missed something and didnt understand, but thats fine, that could be a me problem. I saw the explanation again and understood it confortably. In terms of novelty, I believe this was the most unique video I have seen in this competition up until now, because most consisted animations, this was rather refreshing to see real world objects to actually see through our mathematics.

Really well made video, well done, good job.

Very entertaining and well made. Relaxing background music.

I liked the video! It’s a great example for learning group theory. Sometimes it was a bit technical which might make it to difficult for high-schoolers to understand (which is the indicated audience). But I would imagine that for undergrad math students this works just fine.

Great introduction to group theory with an application. The actual introduction to groups felt a bit too fast, especially if the target audience if for people in high school

fun exploration

I think the walls of complicated equations didn’t really help I think explaining the concepts could have been better

Good pacing, funny, and interesting topic

Great job on your SoME entry! Way to break a children’s game by not just solving it 1 way but solving it in all 655856 ways. 👍

Overall I think the video is well presented. The problem you’re solving is very clear: enumerate all solutions to the Colour Cube Sudoku puzzle. You solved it step by step using combinatorial arguments and group theory. The video also looks polished overall. The lighting on your table is good. The animations have clean and visible colours.

There is just one step that I have trouble following. The main idea of your proof seems clear to me: There are a lot of ways to generate more solutions from a known one. Quoting 11:32, you can have row permutations, row flips, etc. So the proof idea is to put all of these “equivalent” solutions in an orbit, and pick one distinguished solution from each orbit. That I understand.

12:06 In a distinguished solution, I see that the 3 cubes on the main diagonal are all missing red, and the blue is in the top left. In effect you’re fixing a row permutation, column permutation, row flip, and column flip. But what about transpositions? Originally, at 9:00 in the video, you placed the red/orange/yellow/white (ROYW) cube in row 2 column 3. But are you doing the same at 12:06?

In other words, does the definition of distinguished solution include the location of that ROYW cube, or is just the 3 cubes on the main diagonal? If not, then how are you fixing the transposition? Isn’t $|X| = |Y| \times |G|$ true only if you also fix the location of red/orange/yellow/white cube?

In fact, at 13:26, is this why you took the transpose? I wasn’t sure why you needed a transpose. But if you were implicitly fixing the location of the ROYW cube then yes, you would need to transpose.

Also at 13:49, when you cycle green/orange/white, at first I didn’t know why you had to do those row and column permutations after cycling them, since the blues are still in their top left corners. But I noticed that you put the ROYW cube back to row 2 column 3.

Actually, the more I watch it the more I’m convinced that you did mean to fix the location of the ROYW cube. OK, I’ll give this entry a 7. But I really wish this point was made very clear in the video.

This video is a wonderful case study in group theory. I am mildly aware of group theory but have never been formally exposed to it. The video presents core ideas and applies them directly to a real-world object, and it’s a whimsical object at that! Ultimately the video answers the question about the number of total configurations in a satisfying way. Much of the video is black text on white background, and that is hard to follow on a single viewing. Additionally the primary visual aid, the sudoku board itself, does not clearly demonstrate its current configuration, it doesn’t aid in understanding, and it fills the majority of the screen time.