Summer of Math Exposition

Good topic but your voice is a bit too monotonous.

Motivation - it was a motivating video. I like the application to binary math. Also gave a good challenge at the end.

Clarity. Very clear. Nicely done

Novelty - not terribly novel but that isn’t a detriment to this video.

Memorability - the visual graphics and clever questions will make the problem memorable. Nice work!

I really like the introduction, and your visuals look very nice support what you are saying well. I didn’t quite understand the issue at first but then I realized what you’re getting at. I think you could have mentioned where a problem like this may appear in the real world, as I don’t have any context when this could be useful. All in all, interesting and entertaining video about a neat trick.

Great little video! Shorter and to the point, raises an interesting question, and an eye catching thumbnail/title.

Something I would look to improve on is the sound quality and maybe trying different methods to keep the energy and the viewers attention up through the video, which is always a challenge in these types of videos.

It was a good topic and well-motivated. As a few folks have pointed out in the comments, I think you’re underestimating just how natural the ‘rejection sampling’ approach is for this problem, and I feel like presenting it that way first rather than the somewhat more complicated recursive approach that you used would be good. I also had a couple of audio quality issues early on, though those smoothed out over the course of the video. These are mostly quibbles, though; it was a topic I’m already fond of, presented well, and I thouight it was a good video.

(Oh, and to answer the final puzzle, I can do it with an average of under four throws: choose the first item with probability 1/5. This can be done in (on average) two throws by using the standard binary method (toss a coin until you get a result that’s different than the value in the binary expansion of the number; accept if the coin is 0 vs. a bit of 1 in the binary expansion, reject if it’s a 1 on the coin and a 0 in the expanxion). If you don’t choose the first item, run a two-flip tournament to choose from among the other four uniformly. By linearity of EV the average number of flips will be (1/5)*2+(4/5)*4 = 3 3/5.)

I am not going to be too harsh , but your video could be too detailed and also discover some concept for deriving the process for choosing for among n options . John von Neumann (1951) dealt with a related question: how to turn a biased coin into a fair coin (his “von Neumann extractor”) I would hace loved if you had experimented with this in the video

Some suggestion:

1. Improve voice speed and quality
2. The scale used for random number could have been 1 to 10, no need for decimal.
3. The title should have been :Can a Coin Choose Among Three Options Fairly?, else your friends explanation solves the question in title for me.

Keep going.

The overall quality is definitely better than last year!

This is a neat puzzle! Once you brought up the number line, binary search came to mind for me.

It’s clear that you have a good handle on manim. I would suggest looking into ways to improve your audio quality, but that often costs money, and I personally hate recording narration.

Nice setup. Good graphics. Concepts could be explained in simpler terms though.

Thanks for this video using a simple example of painting a room and deciding on a color. Great work too with using Manim for your videos. The Ranking score is an average of these individual scores, good luck: Motivaton: 9 Clarity: 7.22 Novelty: 5 Memorability: 5

A concrete problem, well explained. The two solutions given are clear, the computations are easy to follow, and everything is well illustrated. Having the options be color coded is great.