Logical or Not?

Today's Puzzler was mostly logic based, and required little to no math. Three prisoners are blindfolded. The warden says to them, "One of you is going to get a chance to go free. I have five hats: three white, and two black. I am going to put one on each of your heads." After he placed the hats, he lined them up, and took off their blindfolds. The person in the back could see the two hats and people in front of him, the person in the middle sees only the hat and the person in front of him, and the person in front sees nothing. The warden asks the back man if he know what color his hat is. He doesn't. Next he asks the middle man. He doesn't know either. Finally, he asks the front man, who says, "I know the color of my hat." How does he know? As always, STOP reading if you want to solve it yourself.

In order for the back man to know the color of his hat, the middle and front people would have to both have a black hat, making the back hat white. Since he does not know, the middle and front people do not both have black hats. The only way for the middle man to know his hat color is if the back person does not know, and the front person is wearing a black hat. This is not the case either, as the middle person does not know either. This means that the front person's hat must be white.

After the puzzler we had independent study for about an hour. With all the lessons from the students this coming week, there will not be much time for independent study, so today was our last day of spending a full hour on it. In this hour, I got through another section. I have one more section to go, and then there is another quiz. I have no idea if I will make it to that point or not. It all depends on the amount to time we get.

Afterwards, Dawson lectured about non-classical logic. This kind of logic has a "gray area" as well, instead of just true (1) and false (0). Within non-classical logic, we learned about two types of "fuzzy logic" (Łukasiewicz and Zaden) and two types of "Integer-Based Logic." (Comparative and Sugihara) I found learning all these logics at once very confusing. They are all very closely related, but each has a subtle difference from the others. I had to constantly refer to my notes to solve the problems he gave us. It turned out Dawson's goal was not for us to master these logics, but to simply get a brief exposure to them. These logics are not part of any high school curriculum, and are only used in logic classes in college, so they are not as important as the matrices and probability that we spend multiple days on.

After this short lecture and practice of the different logics, we did more independent study, for about 20 minutes until lunch. After lunch, we did an activity. This was the least math related activity we have done, but it was still lots of fun. Dawson gave each of us a sheet with 30 Rebus puzzles and a corresponding answer sheet. We were given 10 minutes to solve as many as possible. After the 10 minutes was up, he collected the answer sheets to grade, and gave us the next set. There were four sets in total. After we completed them all, Dawson tallied up our scores, and put it on the board. I got 4th place. Then he handed the answer sheets back, and we went over every answer. I was very glad we went over all of them. If we didn't go over it, I would never have gotten to appreciate some of the really clever ones that I missed. Other ones I missed made me feel stupid, as they seem so obvious now, but it's not a big deal.

Study hall was very productive today. We went over about 10 minutes early, so I got a lot of work done. I even had Dawson check various parts of my lesson. He also helped me estimate how long each portion would take and gave feedback on what he thought was a good idea, and what was likely to fail.

Today in Arête, we learned various kicks and strikes. Instead of practicing the moves on our partner, the instructors each held a punching bag. We lined up, and took turns hitting it with the various moves they taught us. I enjoyed this much better than the previous lesson, because the kick and strikes did not hurt us, unlike the pressure point and bone-breaking techniques we learned earlier in the week. Towards the end of class, the instructors had us review the moves we learned through the week. We then had to pick one to perform at the Arête showcase tomorrow. I chose to do one of the many anti-choke moves we learned.

My dinner

After Arête, I put some finishing touches on my PowerPoint, and created an answer key for all the problems I will assign the students. Today's dinner was spaghetti and meatballs, with broccoli, and garlic bread. The food was very good, but there was a very long line to get it. By the time I got to the buffet, they were running out of everything, so I had to wait for them to bring more trays of food.

After dinner, we had SOFT time, but I worked on making final preparations for tomorrow's lesson. It always seems PowerPoints are never done. There's always finishing touches to add.

Tomorrow is going to be awesome. I get to teach the class about mixture problems, and we have our scavenger hunt in the afternoon. The only sad part about tomorrow is that it marks the beginning of the final week of VSA. It is hard to believe that we have been here almost two weeks (officially on Sunday evening.)