Tuesday, March 19, 2013

Happy Mathy Day

I copied Denise's sign, with minor modifications, and got this..

We're both writing in response to David Coffey's post, What's the Point? And all three of us are using the easy peasy sign generator made by a teacher at the real Roosevelt Middle School in Oakland, California.

Why play? Because every day can be a math day.

Wouldn't it be cool if a different math lover made a Happy * Day sign every day for the rest of this month?

Who will do a sign tomorrow?

Friday, March 15, 2013

Pi Day Puzzle Party - Join in, a bit late...

My friend Sharon invited me to head over to the city (San Francisco) on Thursday evening to meet her at a Pi Day Puzzle Party, sponsored by Ask a Scientist. Contestants could form teams of up to 6 people or work alone. The venue was a fascinating spot. SOMA Streatfood Park is an open lot with a pre-fab metal building in the center, surrounded by food trucks (some gourmet, some not so much), buried in a very industrial part of the city. It made me think of a gypsy camp.

I arrived first and grabbed us a (picnic) table. Sharon arrived soon after and we got food from the Peruvian food truck. When the party started, there were about 40 teams, with about 100 people packed into the cozy space.

We were handed the first question face down, and the MC, Wes Carroll, read it it to us all. Then we could turn it up and work on it for ten minutes, before getting the next question. There would be seven questions in all.

Question 1: There is a rare disease, called Anti-Mathitis (AMI for short), that afflicts 1 person in 10,000. There's a 90% accurate test that tells whether you have AMI. This means that 90% of the people who have it test positive and 90% of the people who don't have it test negative. You have just found out that you tested positive. What are the chances that you have the dreaded AMI?
Well, I knew all about this from teaching statistics. Back in the nineties, the state of Illinois required an HIV blood test for people applying for a marriage license. It turned out not to be as helpful as expected, along with being a big expense.

My teammates were working away together, while I wrote out what I needed. Sharon had emailed us messages about how she wasn't sure her 8-year-old friend Pai would like it, because we would be working hard at solving the puzzles and not slowing down to explain. So I knew ... winning was our goal, and my new buddies would be ok with me jumping in to explain my answer. Pai did come, and didn't mind our intense focus at all. We named our team The Pai Team.

Explaining my method showed me my arithmetic mistakes. (No calculator, oh no!) As I was cleaning those up we were handed the next question:
Question 2: There are 100 ants in a line on a 1 meter log. They are all walking on the same straight line. When one reaches the end of the log, it falls off. If two collide, they immediately reverse direction and continue on their way. Each is going at the speed of 1 centimeter per second. How long until all of them are guaranteed to have fallen off the end?
I knew I had seen one like this before, but had no idea how to proceed. I knew I needed to think about making the problem simpler, though... I suddenly had a flash of insight. This time, I waited until my team had finished discussing other ideas before I threw my idea in the ring.

And before we had time to take a breath, we were on to the next:
Question 3: Pat calls out 4 consecutive integers. Chris divides each by her age (a whole number), and notes the remainder each time. She adds the remainders and gets 40. Now Chris calls out 4 consecutive integers, Pat divides each by his age (a different whole number), and notes the remainder each time. He also adds the remainders and also gets 40. What are their ages?
This ended up being my favorite problem. I'd never seen one like it. We were still explaining it to one another when we got the crazy logic problem ...
Question 4: Stuck on an island there are 100 people with blue eyes, 100 people with brown eyes, and one guru with green eyes. Each of these people is a perfect logician, and will figure out their own eye color as soon as it is possible. They cannot speak, or communicate in any way, except for the one time the guru makes a statement. Nor can they find any way to see their own eye color. They each can easily see the eye color of every other person on the island. Each night at midnight, a good fairy comes and takes away anyone who has figured out their own eye color. One day the guru says, "I see someone with blue eyes." Does anyone leave the island? If so, who and when?
We got it...

Then came the red, white, and blue balls. I thought this problem would be our downfall...
Question 5: We have 6 balls that are visually identical except for color. There are two of each color, red, white, and blue. One of each color is heavier and one is lighter weight. All the lightweight balls weigh the same, and all the heavy balls weigh the same. We also have a balance scale. We need to determine which is which with only two weighings.
 We came up with lots of good ideas, but they all ended up requiring three weighings. We had to leave #5 blank on our answer sheet and go on to #6...
Question 6: In the picture at right the square has area 64, and the triangle is equilateral. What is the diameter of the circle?
Hew got us started on this one, and we worked feverishly on the algebra. We got it... (At the end, the MC shared with us all another  way to solve it that requires no algebra. This other way is elegant and beautiful.)

One last question... (Although I think they're out of order...)
Question 7:  You have a pile of coins. Ten of them are heads up, and the rest are tails. You are blindfolded and cannot see them, but you can flip as many of them as you'd like. Can you put them into two piles, so that there are the same number of heads in each pile?
I had heard of this problem before, and probably heard the answer. But I have a terrible memory, and remembered nothing. As we worked on it, nothing made sense. Finally, I saw what needed to happen. And they were giving us twenty more minutes to work on our answers! Back to those dratted balls. I scribbled out my final asnwer just as we were asked to pass our answer sheets to a neighboring team to check. They took my scribbles along with our answer sheet. Whew!

The MC gave the first answer. It was different than ours. I had explained ours so carefully to the rest of our team, I was sure we were right. And the team whose answers we were checking had the same answer. So I raised up my hand, and the MC said, "Ahh, we have some dissent." He called me up to the microphone. Of course, there was a chance I was wrong, and I was shaking with nervousness.  But I explained my thinking to him, and he agreed, and there were cheers. (When have I ever been cheered before for the answer to a math problem?)

We answered all 7 questions correctly, as did the team sitting right next to us. It turned out they and we were the only two teams to get them all correct. So our two teams were asked to send a representative up front for a tie-breaker question. We had to stand on chairs to be seen by the crowd. The MC warned us that a wrong answer would give the other person plenty of time to think.

The Final Tie-Breaker Question: What is the smallest prime factor of 317+523?
I saw the answer, said "I know it", and won the contest for our team! I was stoked. I have never done a math competition before, and I'm not particularly fast, so I hadn't dreamed that we'd win. My teammates came up, and photos were taken. It was quite a scene.

I asked the other team if they had recognized any of the questions. No, they hadn't. I told them they had really won then. Even so, we were full of the thrill of victory as we made our way homeward, and delighted to have shared it with 8-year-old Pai. None of our questions had had any relation to the number pi, so we were very satisfied to hear about her part in the  Pi Day parade at the Exploratorium. Pai and her mom held up the 95th and 96th digits of pi, both 1's.

Celebrate Pi Day a bit late, and answer these 8 puzzle questions. (Please, no answers in the comments.) I'll send a fun math book to the first person to get all 8. (No fair using Google. You are on your honor.) Teams are fine. Send your answers to mathanthologyeditor on (use the letter after f, along with mail). Your last puzzle is to make sense of my email, that I'm hoping to keep away from the scambots.

Saturday, March 2, 2013

Carnival of Mathematics #96

Question for psychics and detectives: I once got 96 points in Scrabble for a four-letter word. Can you guess what it was and where it sat on the board?

Puzzle: Use the numbers 1 through 5 once each to make 96.

Reader Participation: Can you offer us a harder puzzle related to 96?

The Math
Anna Weltman, at Math Munch, posted about Marjorie Rice's discovery of new pentagon tilings of the plane (back in the 70's). The cool factor? "Marjorie had no mathematical education beyond high school." And, if I'm doing my arithmetic right, she was over 50 when she made her discoveries.

Brent Yorgey, at The Math Less Traveled, wrote Visualising Pascal's Triangle Remainders, originally as a comment on Katie Steckles' piece at The Aperiodical about Singmaster's Conjecture, which was in response to a throwaway line about coloring in Pascal's triangle. It involves some pretty pictures!

Patrick Honner, at Mr. Honner, wrote How Many Primes Did We Miss? in response to a student's wondering. He says, "During a discussion of the new largest-known prime, a student wondered if there were any primes between this new largest-known prime and the previous largest-known prime. Thanks to Bertrand's Postulate, we know there are quite a few primes between them!"

Kurt Friedrich Gödel, at Ciencia y Lógica son suficientes, wrote a post on Gödel's Theorem. He gives an actual example of a formal system by using kinships, so that the theorem and some logic terminology can be better understood. Y en español, nos ofrece Series Gaussianas. "Trata sobre el desarrollo de distintas demostraciones entorno a las series de potencias de números naturales, tales como la progresión 1+2+3+...+n, la correspondiente al teorema de Nichomacus, y en general para cualesquiera potencias."

Evelyn Lamb, at Roots of Unity, wrote Romance, Continued Fractions, and You as a Valentine's Day post about a dream in which continued fractions were a metaphor for love. I'm afraid the romance may be all in her head, but her article is fun and does a good job of explaining continued fractions. Evelyn's been busy lately, and pointed out two other posts. She explains what Roots of Unity are, besides being the name of her blog, and she posts a wrap-up on the Joint Mathematics Meetings in San Diego.

Matthew Barsalou, at Significance Magazine, wrote Keep Your Redshirt On: A Bayesian Exploration. Star Trek fans, take note.

John Cook, at The Endeavor, posted a Probability Question a while back that kept me thinking. More recently, he's been posting a series on damped and undamped vibrations. (If I ever get around to teaching differential equations again, I'll want these.)

(by Brent Yorgey)
Math Education 
After moderating a conversation at Educon in Philadelphia in January, and reading about some good ideas on math curriculum (from Henri Picciotto) and lesson planning (from the Bacon-Wrapped Lessons project), Mike Thayer, at Hyperbolic Guitars, started to think some more about what a math education might mean nowadays.  On My Mind reflects the most recent evolution of his thinking.

Patrick Honner, at Mr. Honner, (also) wrote Regents Recap — January 2013: Unstated Assumptions, in which he questions the Regents exam for encouraging students to make assumptions without stating them. Good discussion in the comments.

Pat Ballew, at Pat'sBlog, explores the history of the m in y=mx+b, in Why m for Slope. "One of the most asked questions by students and other teachers, and a topic of more dubious history than almost any other in math." Pat also wrote Tally Sticks, Keeping Count through the Ages. "From wolf bones to dominoes, people have been using tallies to keep count. A brief history includes burning down Parliament and some modern approaches."

Oluwasanya Awe, at MatheMazier, wrote Let's Get Talking. "Education in secondary schools is really not in the best state at the moment. This post presents some questions that a high school students ask and indirectly shows mindsets of how teachers and students see Mathematics in school." I would love to see some blog posts written in response to these quotes. Do any of them hit home for you?

Interviews, Reviews, Links, ...
Sol Lederman, at Wild About Math, does a series of podcast interviews called Inspired by Math. Sol was intrigued by Jason Ermer's Collaborative Mathematics project, which encourages people to think deeply, in groups, about open-ended problems, and to share their insights with others via Youtube video responses. So he interviewed Jason for Inspired by Math #23 (22 minutes long) about what the project is, what inspired him to create it, what the response so far has been, and what he is hoping to accomplish.

Shecky Riemann, at his new blog, Math Tango, wrote Statistics Is Suddenly Sexy, in which he reviews Charles Wheelan's latest, timely book for a general audience, Naked Statistics.

Stephanie Glen  is involved in a kickstarter campaign for an educational TV show for preteens about math. "The Number Hunter" is a cross between Bill Nye The Science Guy and The Crocodile Hunter -- bringing math to children in an innovative, adventurous way. She's hoping some of us will be interested in helping kickstart it.

Tony Mann, at Tony's Maths Blog, wrote Are Mathematicians and Artists Opposites? He doesn't think so. What do you think?

How do you find more? Subscribe to one of the many blogs that collect links to mathy goodies:  Math Munch, Aperiodical, Wild About Math, Math-Frolic, God Plays Dice, Math Blogging, ... (Who am I missing?) And check out previous Carnivals of Mathematics or Math Teachers at Play.

The next Carnival of Mathematics will be hosted at Flying Colours Maths (and last month's was at Math's Fact). Submissions are accepted at the submissions page.

Countdown: 12 days until Pi Day. (Unless you prefer to celebrate Tau Day.)

Answer to Scrabble question: The word was 'quiz'. It was at the top of the board, but I couldn't find a picture of that. Here's an equivalent position: 
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