Here is how I spent one of my spring break days (yesterday). First, I wrote up a draft of a paper. Then, I proceeded to look at three coin problems.
Suppose that you are sitting at a square table with an upside down cup on each of the four corners. There is a coin under each cup. Your goal is to make it so that either all four coins are heads, or all four coins are tails. Here are the rules:
There will be "turns." Each turn, you are allowed to pick up any two of the cups, and then change those two coins to be in whatever orientation you like (e.g. heads/heads, tails/tails, heads/tails, or tails/heads). Once you put the coins down (and the cups over them, again), one of two things happen: either all four coins are matching, which is indicated by a light going off in the middle of the table, or the table spins around. When the table spins, you are unable to follow it because it is spinning so fast. The table will stop, and you will be allowed another "turn." You may, again, pick any two of the cups, although you will not be able to tell which cups you looked at last turn (because of all of the spinning). Continue this process of picking two coins followed by the table spinning until you have won.
Question: is there a strategy that will allow you to win without getting lucky? If so, what is it? You should assume that you have the worst luck in the world, and cannot ever say "eventually I will have to win with this process."
If there is no such strategy, prove that there is no such strategy.
(this was from an email from one of Skye's friends)
Assume that you are sitting at a table, blindfolded and gloved. On the table in front of you are some number of coins. You can feel the coins well enough so that you know how many coins there are total, but you cannot feel them well enough to determine if they are "heads" or "tails" (because of the gloves). Suppose also that someone tells you how many "heads" there are on the table. So you know the total number of coins, and the total number of heads, but nothing else. You can pick up any of the coins and flip them over, and you can repeat this process as often as you like. You can do nothing else.
Question: can you sort the coins into two piles so that each pile contains the same number of heads?
(this was from a book by Ed Burger)
Suppose that you have 12 coins that look absolutely identical. In fact, 11 of the coins are completely identical. The 12th coin is counterfeit, and weighs either just a little more or a little less than the other 11 coins. You do not know which coin is the counterfeit.
Your task is to find the the counterfeit coin by using a balance (one of the old scales that you see kicking around the justice department). Can you find the counterfeit coin by only doing three weighings (or fewer)?
(this is an old problem that hangs around math, physics, and computer science departments. I had solved it before)
You have 10 bags of gold coins, 10 coins per bag, 10 grams per coin, but one bag of coins weigh only 9 grams per coin (because of low quality). How do you find out which bag contains low quality gold coins? You may use a scale (now a bathroom-type scale, rather than a balance) only one time.
(another oldie. I had remembered this solution, so that wasn't much fun).
Then I started to look for other problems. I went to Just Riddles and More (which has a completely ridiculous name), and found this problem:
Q: You have 9 gold coins. All 9 coins look exactly the same but one coin is a fake and is either lighter or heavier than the other 8 coins. You have a scale - balance type with 2 trays - but can only load it twice. How do you find the fake gold coin?
I worked on this for a while, and decided that it was probably impossible. I was right. The solutiontotally cheats. This frustrates me. Then I noticed some alternate solutions to problems similar to the ones I asked above, and they were solved similarly. Some people should not be allowed to have webpages. I should have known not to go to the website just by the web address.
I now think that it is possible to have an extremely practical electric vehicle (top speed of 100 mph, range of 100 miles) for under $20,000. A lot of people are converting old Porsche 914s for this purpose.
This story is one apostrophe away from being great.
Yahoo! has a story about the tallest man alive (this story contains feelings for those of who think that this weblog is only about sports and politics). Apparently they have never heard of Leonid Stadnik, who is about eight feet four inches tall.
Today was spring cleaning, and the spring has been cleaned. I had a major revelation today that has left me quite pleased. I realized that I can simply air dry my laundry, rather than using the dryer. This makes me exciting for three reasons:
It costs less money.
It is environmentally friendly. Less energy is used, and no pollution.
No quarters are used. This is different from the first item, since I sometimes am unable to do laundry because I do not have enough quarters.
I went to Target and I bought some drying racks. Jill helped me out.
This is exciting for me.
I also bought a shredder, and went through all of my old paperwork. My place is now reasonably clean.
Curses. UNC lost. I want to blame Georgetown for cheating, the refs for being unfair, or bad luck. The fact of the matter is that UNC was just terrible over the last 12 minutes of the game. Absolutely terrible. They were forcing shots, didn't take it at Hibbert (who had three fouls at the time), and couldn't stop Georgetown from getting good shots. Lawson should have been driving and dishing a lot more than he was. It was just awful - painful to watch at the end.
Not only that, but my bracket went down the tube. I picked UNC to win it all, and I only got two out of the Final Four correct (I had Florida and UCLA, but I also had UNC and Texas A&M). It was a good year for me until the end of the tournament. I think that I have an outside chance of winning my office pool, but I am not counting on it.
Here is a good idea for teachers who teach any sort of math: the AWM Teacher Partnership program. I just signed up.
I did my taxes, and I am going to get some phat money back from the Feds. This is because my entire income goes toward paying off my mortgage interest, so it is like I have no taxable income at all. This means that I should be able to pay off my second mortgage in about a week. I am a little disappointed that I won't be able to chip away at it month by month like I have been doing (I am only 2-3 months away from being done), but I think that I would rather just be done with it than have the satisfaction of the chip-away. Now, I can start saving money again.
This has been kicking around WestWash for a while, but I like it.
Help is on the way! Of course, Bush will veto it if it gets to his desk, but this is a step in the right direction.
Actually, I am not sure that this is a step in the right direction, since I don't know what to do with Iraq (although I know that we shouldn't have initially invaded). Ultimately, I think that this is the right thing to do because I think that our presence is causing more problems than it is solving. I am also guessing that the neighboring nations would step up and help with Iraq's security (since it would be in their best interests).
While I'm talking about politics, the following video is just plain frustrating. This reminds me of when I taught in the high schools. From time to time, I would see one of the boys throw a crumpled up piece of paper across the room. I would immediately ask him about this, and he would immediately EMPHATICALLY deny that he did this. Everyone in the room saw him do this, including me. Why wouldn't you just admit that you were caught? Did the student think that I might reevaluate my ability to interpret the information that comes in through my eyes? Doubtful.
Anyway, Tom Delay is that 15 year old in my classroom who throws crumpled up paper across the classroom. Just frustrating.
What a week. There was a stretch of six days where I spent at least part of the day in a different state. Traveling is over for a little bit, though, and I am ready to rest up and recover.
I think that I ended up getting 40 out of the first 48 games correct in the first two rounds of the NCAA tournament. I picked three out of the four games correctly last night, bringing my tournament total up to 43 out of 52. However, there was a casualty. I picked Texas A&M to go to the final four, and they went down. I think that they probably got screwed - it looked like there was no way that that last tipped pass took 1.1 seconds off of the clock (unless Greg Gumbel was correct that the ball bounced in bounds first). An extra 0.7 seconds would have allowed A&M to get inside the three point line for a makeable shot. Little bitter.
Spring break starts in about seven hours. It will feature: work.
I spent the weekend in St. Louis at a group theory conference, and I am leaving to give a seminar in Athens, Georgia today. I'm just going to give you a quick update:
I ended up getting 29/32 correct in the first round of the NCAA tournament, and only 11/16 correct in the second (it should have been 12 - I meant to pick Tennessee over Virginia). However, I still have all of my Elite Eight teams in play, so it could be worse.
Also, I am leading the office pool right now, but a couple of people are catching up on me.
I made my NCAA picks today. I felt like I could do this, because I completed slides for my talk in St. Louis this weekend. I still need to do some severe editing, but this is a major accomplishment. After that, I need to get my talk for Tuesday (in Athens, Georgia) ready.
My picks for the first round: Florida, Arizona, Old Dominion, maryland, Winthrop, Oregon, UNLV, and Wisconsin in the Midwest Regional. I picked Kansas (over Niagara), Kentucky, Virginia Tech, Holy Cross, VCU, Pitt, Indiana, and UCLA in the West. UNC, Michigan State, USC, Texas, Vanderbilt, Washington State, BC, and Georgetown in the East. Finally, I picked Ohio State, Xavier, Tennessee, Virginia, Louisville, Texas A&M, Nevada, and Memphis in the South.
My day students have a midterm today, and my night students have a midterm tomorrow night. Combined with my trips to St. Louis and Athens, this makes for a busy week.
I spent the weekend in North Carolina at a math conference. It was good, athough there were severe airport problems both to and from the conference. Fortunately for me, I plan ahead, so my travel plans were not disrupted (much).
Sorry I missed Byron in Huntersville. That would have been nice.
I have a lot of work, and a short time to do it. I'm East bound...
No Studio 60 tonight. I get the sense like there may never be another episode (although they have already made one more that has not been shown).
I have a lot of stuff to do. Primarily, I have to write an exam, finish my research, prepare two different talks, and entertain folks from out of town. All of this should happen in the next two weeks (including grade one, possibly two exams).
Life will be a lot less hectic starting on March 21st.
I had my first "Six Feet Under" dream last night. That is, I had my first dream where a dead person reappeared, and it was realistic enough that I (at least, my dream self) was confused as to whether it was real. I dreamed that my recently deceased grandmother was visiting us at my parents' house. It was interesting because it was so mundane, it confused me. It was my mom, dad, aunt, grandma, and I sitting around the living room talking. This was nothing otherwise interesting about it.
At some point, I began questioning if this was real or if it was a dream. I started to look for clues that it might be a dream. I looked outside, and noticed a great deal of detail that I don't normally notice. I noticed cars parked in the driveway. They were coated with salt, as cars often are in Minnesota winters. I can still see how the salt streaks ran down the car.
Finally, I noticed something. The houses across the street were different from how they are in real life. For instance, the house where our friends A, N, and P grew up was red and three stories. This clinched it - it was a dream.
Also, this again confirmed that I do dream in color.
