Thursday, July 25, 2013

For Every Beginning There is an Ending

My last full day of VSA started at 7:45 AM. I went to breakfast at 8. For the final time, class started at 9, with another Puzzler: You and a friend are playing a card game. There are 21 cards in the deck (it does not matter what cards.) We alternate taking 1, 2, or 3 cards per turn. The person who takes the last card(s) wins. In each turn you must draw at least 1 card. (You cannot pass.) Is there a strategy to win? What is it? For the second to last time, STOP reading if you want to solve it yourself. (Wait... There's another Puzzler? Keep reading to find out...)

Dawson had us solve this Puzzler by playing the game. He had us get into pairs, gave us 21 cards, and had us play the game for a little while. We soon figured out that if there is 1, 2, or 3 cards left, and it's your turn, you win. If there are 4 cards left, you loose. If there are 5, 6, or 7 cards left, you win. If there are 8 cards left, you loose. If you continue this, you find that if the number of remaining cards is a multiple of 4, you lose. This occurs no matter how many cards you take, your opponent can stick you with a multiple of 4 again, until you get 4 left and lose. (If you take 1, he takes 3. If you take 2, he takes 2, and if you take 3, he takes 1.) After we figured out the strategy, we had beat Dawson. It took me multiple attempts, because the first time he went first and took one card. This left me with 20, and a loss already. After I finally beat him, he had me come up with a strategy to win if there were 21 cards, and you could only take 1 or 2 cards per turn. In this game, you want it to get down to a multiple of 3 (because 1 + 2 = 3). This means the best strategy is to not go first. Since 21 is a multiple of three, it does not matter whether the first person pick 1 or 2, the second person can match it and stick the first person with another multiple of three until the end.

After spending 30 minutes on the Puzzler, we watched A Beautiful Mind. As I said yesterday, the movie is about John Nash, the mathematician that came up with the Nash Equilibrium. The movie starts in his college years at Princeton. He does not attend class, because he wants to create an original contribution to mathematics. He spends almost all of his time working, so his roommate (Charles) tries to get him to get out and go to bars and such. He is very socially awkward. Every time he tries to pick up a girl, it fails miserably. On one of the bar trips, Nash comes up with the Equilibrium. 5 girls walk in the bar, one (a blonde) is much prettier than the rest. Nash's four friends believe they should all go after the blonde, because according to Smith's philosophy, what's best for the group comes from everyone doing what's best for himself. Nash proves this wrong: If they all go for the blonde, they will get in each other's way, and no one will get her. Then if they go after her friends, they will feel second rate, and leave. If no one goes for the blonde, and they each go for one of her friends, everyone gets a girl.

Nash writes his paper on the Equilibrium, and publishes it. He gets a job at Princeton's Wheeler Laboratories. As part of his job, he must teach a Calculus class. One of his students falls in love with him. Soon after, the government hires him to break codes the Russians are sending. He is extremely good at this, and is able to find the coordinates of an atomic bomb from the millions of numbers in the message. The military then has him crack more codes. This time, the Russians are communicating through periodicals (TIME, Newsweek, etc.) This mission is classified, so he cannot tell his girlfriend, who eventually becomes his wife. When turning in one set of his newspaper findings, he and his agent Parcher get caught in a Russian shoot out. From this point onward, Nash is constantly paranoid that the Russians are after him. Eventually, Nash is taken to a psychiatric facility. He thinks the doctor is a Russian interrogator, so he tries to attack him.

The doctor diagnoses him with schizophrenia. Parcher and Charles (his roommate) are not real, just images in his head. He is given insulin shock therapy to help cure him. Once he is released, he has to take medicine to keep the illusions away. He does not like the side effects, and stops taking the medicine. When giving the baby a bath, he thinks Charles it watching, so he leaves the room, almost drowning the baby. He also attacks his wife when he thinks Parcher is lounging at her. After this, he realizes that Parcher and Charles are just his imagination. He decides not to take the medicine, but to ignore them instead. He goes back to Princeton and asks his college rival Martin (now Head of the Mathematics Department) for a position researching and auditing classes. After years of doing this and ignoring Charles and Parcher, Nash gets a teaching position at Princeton. In 1994, he wins the Nobel Prize in Economics for his Equilibrium. I really enjoyed this movie. It was highly related to math, but did not make you think a whole lot about it. It was more focused on how sad is was the such a brilliant man had schizophrenia. I found out afterwards that this movie won four Oscars: Best Picture, Best Director, Best Adapted Screenplay, and Best Actress in a Supporting Role. I highly recommend watching the movie, even if you are not into math like me.

After the movie ended, Dawson handed out his comments on our lessons. He also recognized each person for something different. The awards included Best Lessons (1st, 2nd, and 3rd), Best Lesson Plan, Best Dressed, Best Mission, Best Explanation, etc. I won the Best Explanation award for helping a student with her mixture problem during my lesson. She had no idea where to start, so I walked her though the whole thing. 

During lunch, I read Dawson's comments. Overall, he like my lesson. The first 25 minutes were good, but the last 20 when I handed out the worksheet failed miserably. His main suggestion was to do easier problems, which I completely agree with. I assumed too much when I made that worksheet.

My Last VSA Lunch: Fruit Salad, Chili, Pizza and a Breadstick.
After lunch, we had our final puzzler: There are five pirates who steal exactly 100 gold coins. They go to a safe haven to distribute the gold among themselves. Being democratic pirates, they decide to vote on how to do so. Each pirate in turn submits a proposal for parceling out the booty. Immediately after the first proposal, they vote. If the proposal wins a majority of votes (more than half), they distribute the gold according to the proposal. If the proposal does not get a majority, they kill the pirate for suggesting it and move on to the next pirate, who makes his proposal. The process continues until a proposal receives a majority of votes.

You are the first pirate to make a proposal. What should you suggest to maximize your share and, of course, remain alive? You may only presume that a pirate will vote for a given proposal if it is definitively better than another proposal that he may receive. Each pirate knows his own and everyone else's position-first, second, third, etc. in order of giving proposals. The pirates are entirely logical and unemotional people. All they care about is maximizing their share while remaining alive. For the last time, STOP reading if you want to solve it yourself.

Since this is one of the hardest Puzzlers, Dawson had us work in the same groups as the Unknown Area Project. Initially, we assumed that the pirates would divide it evenly, so that the 2nd pirate offers everyone 25, the third offers 33, and the 4th offers 50 each. So the 1st pirate should offer the 2nd pirate 26, the 3rd pirate 34, and the rest to himself. Dawson told us that this offer would not win a majority of votes. 

We then worked backwards. If there is one pirate left, he gets all 100. If there are two left, the 4th pirate will settle for giving the 5th pirate everything, because without the 5th pirate's vote, the 4th pirate dies. If is better to be alive with no treasure than dead with no treasure. When it comes down to the 3rd pirate, the 3rd pirate gets 100, and the 4th gets his life. The 2nd person can buy the 4th's vote with 2 coins, and the 5th pirate's vote with 1 coin. This means the 1st pirate can get 97, and buy the 3rd and 5th's votes with 1 and 2 coins respectively. 

Once we solved the Puzzler, we each go to take 8 pieces of chocolate from Dawson's collection of 100   chocolate "coins." After we had all solved the Puzzler, Dawson briefly explained what would happen if you continued this problem with more and more pirates. There is a recurring pattern. The number of coins the first pirate gets decreases by 1 coin every 2 pirates added. Eventually, the first pirate gets nothing but his life, but there are certain numbers, like 201 pirates, in which the first pirate gets one coin, even though at 200, the first pirate gets nothing.

My portion of the Pirate's Booty!
Dawson and I
After the Puzzler, Dawson had us do another Concept Map about Math. (Just like we did on the first day of VSA.) Many of the students complained, so Dawson told us that the concept map is a VSA requirement. He did not create the assignment. After our 10 minutes to complete it, we filled out a survey about VSA, covering everything from class to your proctor to social time. I forgot the exact wording of my favorite survey question, but it basically asked if you are less socially awkward because of your experiences at VSA. I would never have guessed that there would be a question like this, but there was. 

At the end of class, we took another set of group photos: one with Dawson and the class, and one with Emily and the class. Afterwards, I got a picture with just Dawson. On the way out, Dawson had us put our name and phone number in a spreadsheet on his computer. He said he would email the list to all of us, so we can contact each other. He also mentioned that if we ever want a letter of recommendation, to just ask. He even went as far as to say he enjoys writing letters of recommendation. I will definitely be asking him for one in a year for my Vanderbilt application.

Immediately after class we headed to the Wyatt Rotunda for the closing ceremony. This consisted of various faculty members from the Program Coordinator to the Housemaster to the Proctors saying how much they enjoyed this 3 weeks, and how fast it flew by. At the end of the ceremony, they recognized the rising seniors that did VSA for 4 or 5 years. (You can participate in VSA for up to 6 years, from the beginning of middle school to the end of high school.) The 4 years veterans each got a Vanderbilt mug, and the 5 year veterans each got a t-shirt that said Vanderbilt on the front and VSA 5 on the back. The closing ceremony took an hour, so we had free time from 4-6.

During this time I began my packing. I'm only about halfway done, as there are a lot of things I cannot pack until tomorrow, like my be linens, by towels, and my dirty clothes. The last dinner of VSA was at 6 PM.

My Last VSA Dinner: Salad, Mac and Cheese, Fried Eggplant with Pasta Sauce, Squash and a Brownie. 

My proctor Hugh and I, dressed in suit and tie.
After dinner we had an hour to prepare for the Decades dance from 8-10. I didn't know what to wear, so I ended up dressing in my suit and tie. It turned out my proctor, Hugh Schmidt, was dressed the same way. When we got to the dance, I took a picture with him. I did not enjoy this dance very much either, because again, I'm not a dancer. At the end of the dance, the Housemaster announced the winner of the House Cup. A-House won with 459 points, over S-House with 459, and V-House with 400. After the winning house was announced, all the A-House members started cheering "A-House," and Hugh (because Hugh is the head of A-House.) We then found our proctors and went back to Hank as a group.

Once we arrived at Hank, we had free time until our final proctor meeting at 11 PM. Tomorrow breakfast is at 8, and that we have free time in Hanks from 9-12 (or until we leave.) Mr. Mannix is going to pick us up at 10:30. Hugh also handed out VSA "Yearbooks." (Just like a regular yearbook, with pictures of out classes and proctor groups.) I also found out that the running group will be running one last time tomorrow morning at 7. I guess I was wrong when I said Wednesday was the last run.

VSA is officially over, and I'm sad to have to let it go. I really want to go back in time 3 weeks and do it all over again and again.

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