## Intel STS, Day 2

(5:30) I was actually awake at 4:30 am (probably a bad idea to have gone to sleep at 12:20 am), and just lied down in my bed for about half an hour – I’m very excited and nervous for today, because it’s judging. Yesterday night, I was in Demetri’s room with four other awesome finalists, trying to answer questions and learn stuff from each other. It turns out that I don’t know much biology (which isn’t surprising, actually), so I’m really hoping that if I get any questions on biology (I know I will) then they won’t require too much technical knowledge. I was also at the quad, playing cards against humanity (I’m not the best at it). I think I have two judging sessions today, and three tomorrow. Right now, I’m just trying to review some stuff by browsing Wikipedia, although I’ll probably go and shower sometime soon.

(11:40) I just had my first judging interview, and it actually wasn’t very bad. The first judge immediately began; I forgot what the first question was, but here’s the second question (from the first judge): why don’t satellites fall? I told him that they’re in free fall, but then I messed up and started talking about centripetal force. I should have said that the translational velocity is the same as the velocity during free fall. The third question asked by this same judge was: given 100 tennis players, how many matches do you have to play to get the winner? I told him that the optimal strategy (there could be mistakes, but diregard those) was 99 matches. The reason is, there are 99 losers, and one loser per match – so 99 matches is the optimal strategy.

The second judge asked me about friendship networks, and I told her that they were directed graphs. Then she asked me to compare it to the food chain, which was not too hard. She then asked me to describe how I would represent such a graph in a computer. I told her: given an input (a person), assign him/her a node (two people, say 0 and 1), based on whether or not they consider the other person a friend. This would give you a graph which a computer could understand. She then asked me, how would you write this as a matrix? I told her that we do the same thing as above, except with a square $n\times n$-matrix, where the $(i,j)$th entry is $1$ if person $i$ and person $j$ are friends, and $0$ otherwise. She then asked me, given two people, count the number of mutual friends, including the trivial friendship between the two, if it exists. I gave a rather trivial bound, namely it has to be some integer between $0$ and $n-2$ (because there are two people in consideration).

The third judge began by asking me why, if a car is put outside, in a temperature that’s not freezing, there could be frost. Uhhh … I didn’t know. I asked him if the windows were open, if it’s been to a cold place before, etc. but he told me that it has nothing to do with the state of the car. He gave me a hint, saying that there were no clouds, but I still didn’t get it. He then asked me another question: look at this carbonated drink. It’s bound tight. When I open it, why does the carbon bubble up? I told him that there’s high pressure inside the bottle before it’s open; when it’s open, the air rushes out because there’s low air pressure outside. To fill up this gap in the air’s volume, the carbon forms bubbles and comes out of the drink in the form of $\mathrm{CO}_2$. All in all, it didn’t go as bad as I thought it would,  although I do think I messed up in the very first judge’s questions. Well, I’ve got another judging session at 3:00, so I’ll continue later.

(13:00) I just remembered the first question from the first judge. Given a point A, a river below A (say in $\mathbf{R}^2$), and another point B above the river, what is the shortest path from A to the river to B? I said that you choose the point C on the river such that the angle ACB is $90^\circ$; the path ACB should be this path. The judge nodded and continued with his next question; during lunch, Meena told me that that wasn’t always the optimal solution. Rather, what one should do is reflect B across the river to get a point B’, and draw the shortest path from A to B’; this gives the shortest path as required by the question.

(18:21) So I just finished my second round of judging; it was pretty fun! The first judge asked me how many ways there were to schedule the 40 finalists in the 5 judging rooms. I stumbled, and he told me that nobody’s been able to solve it today. I did a key step which he said nobody’s done, and then he turned it over to the other judge. The second judge began by telling me that when a food company removed glucose from food, the food was still healthy. But when the put fructose, people began dying. I said that they have a different ring structure, but didn’t conclude that the human body couldn’t metabolize fructose, I wasted a lot of time in this question. He then asked me about why baking powder made breads grow; I told him that it was an acid-base reaction, and he told me that that was exactly right, and was very happy. The last question was how neurons communicate with one another, and I answered that they do so via pulses of energy. I made an analogy to computers. He then asked me why neurons are faster than computers; this was quite easy, because neurons have more dendrites than computers. He seemed satisfied, and told me that I did pretty well. This was my last judging session for today, so I can relax a bit until tomorrow, when the first room has a judge in pure math (but I’ve heard that he asks combinatorial questions, which is very hard for me).

(21:10) I just reached my room after a very enjoyable dinner, where we ate with the judges. I was seated with the math judges, which was really cool. It was great to see that the judges weren’t as intimidating as you’d expect them to be in real life, after the whole judging interview stuff. There were two nice speeches about what lies ahead for us (for life in general), and it was inspiring to hear stories from a previous STS finalist who was a health policy advisor for Obama. We then had a professor from MIT’s Lincoln Lab, who told us that all of us would be getting planets – with the exception of those who already got some (so me, Demetri, Amol just hung out and ate the Capitol Building’s dome and the White House’s roof (made out of milk chocolate!) when others were getting their planet certificates).

During dessert, I talked with one of the judges, who’s friends with Jacob Lurie, a mathematician who I admire a lot. He told me about how the IMO changed when he (the judge) was an STS finalist, and a little bit about his projects. I also talked to the other judge who asked me about friendship networks, and I told her that in order to number of mutual friends, I had to take a product of the matrices, but I didn’t elaborate. Then I talked to a few other finalists about my project, and in turn learnt a lot about their projects. It was then time to clear the dessert hall, and some finalists went to the Intel Quad, while I came back to my room, to freshen up. I think I’m feeling sleepy, but I’m not really sure; I guess I’ll just head down to the Quad for now, and try to relax for judging tomorrow (when I have the first slot at 9:00!).

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