Congratulations to your daughter! I just looked over the list of previous winners, and it's an amazing group of women.

Yes, it's a challenging problem, which is why it's starred and has a hint at the back of the textbook. If you or your 14 yo is interested in further properties of Pythagorean triples, check out Euclid's formula on the Wikipedia page: https://en.wikipedia.org/wiki/Pythagorean_triple For example, we can use Euclid's formula to solve the problem you posed here (find a Pythagorean triple with hypotenuse 97). Using Euclid's formula, we just need a way to express 97 (not 97^2) as a sum of two squares, which is easy (9^2 + 4^2). Once we do that, we can determine the two legs: 9^2 - 4^2 = 65 and 2*9*4 = 72.

I don't think the solutions manual says that 97 + b and 97 - b must each be perfect squares. My copy of the manual says: "Since (97 - b)(97 + b) must be a perfect square, we try to find values of b that make both 97 - b and 97 + b perfect squares." In other words, it's merely saying that if 97 - b and 97 + b are perfect squares, then their product (97 - b)(97 + b) is a perfect square. And fortunately, we can find b such that 97 - b and 97 + b are squares.

You may be referring to the case of Cordell Jude shooting Daniel Adkins. I believe Jude was charged with and convicted of manslaughter: http://www.phoenixnewtimes.com/news/cordell-jude-guilty-of-manslaughter-sexual-snub-leads-to-prison-sentence-and-more-6661359

Maybe this depends on where you live? I live in the Boston area, and here as long as it's legal to ride a bike on the sidewalk (legal most places around here except central business districts), it's legal to ride in the crosswalk. It looks like you're in California. Here's a blog post that claims with evidence that in the Los Angeles area, it's legal to ride a bike in a crosswalk: http://bikinginla.com/2016/02/18/attorney-solves-the-great-mystery-of-the-no-biking-in-crosswalk-signs/

My daughter chose Harvard over MIT (and Stanford and Princeton), and was a computer science major. You can get a excellent computer science education at Harvard now; it's come a long way in that specific field. I may be a bit biased because several of my friends are computer science professors at Harvard...

He got his bachelor's and master's degrees from Penn State, and he's currently doing his PhD at MIT during the football off-season. I've seen him at our math seminars.

Yes, the AoPS errata pages are updated as necessary, with any new errors fixed in the next printing of the book. Here is the link to the errata pages: http://artofproblemsolving.com/booklinks If any of you finds an error in one of the books, you can report it to the email address listed on that book's errata page. If it's for the Prealgebra book specifically, you can alternatively message me. It's been more than 2 years since we last found an error in the Prealgebra book.

I've used Cozy for more than a year. I agree with Stephanie: it makes rent collection easy and automatic for you and the tenant.

I'm a Research Affiliate at MIT's math department. I'm not a professor, but if you send me a PM, I could try to help you and your son find a professor or two to talk with.

Cool! Yes, we enjoy the Cupecoy area of St. Maarten. We originally moved to the island because my wife became a professor at the medical school (AUC), which is in Cupecoy. At first, we were renting an apartment at Rainbow Beach Club in Cupecoy. Mullet Bay Beach, perhaps the nicest beach on the Dutch side of the island, is walking distance from Cupecoy. I like areas where we can walk to various activities. So in addition to Cupecoy, I would consider Simpson Bay and Maho. Good luck!

We live (lived) on the Dutch side of St. Maarten, close to the border with the French side. There is no border patrol; we'll often drive (or jog or bike!) to the French side. Our condo is in this resort: http://www.portocupecoy.com There are other housing options that are more affordable. Yes, gorgeous is the word I'd use. English is the primary language on the Dutch side. On the French side, you'll hear a mix of French and English. Neither I nor my wife know French. Well, I took it in high school, but alas forgot most of it. When on the French side, I try to use a few French words (e.g., Bonjour or Merci) out of politeness, but otherwise will communicate in English. If you decide to visit the island for research purposes, let me know and you might be able to stay in our condo.

My wife and I lived on the island of St. Maarten (St. Martin) for 3 years. We still own a condo there, and will be there this January and February. It's a fun island.

My wife and I live in Somerville, Massachusetts, less than 5 miles from Boston. We don't own a car and don't want or need one. We get around by walking, taking the subway, taking the bus, riding a Hubway (the city's shared bikes), riding our own bicycle, taking an Uber/Lyft car ride, or renting a Zipcar by the hour. Housing is not cheap here, but the lower transportation expenses help keep the overall cost down. We love it. We get automatic fitness by just walking or riding a bike. About where to live in the Boston area, that depends a lot on where exactly your husband finds a job. Good luck!

Yup, I took the Olympiad Geometry course. Geometry is my weakness, and the course was challenging!