## A challenging 11111… puzzle

I received this email from Mr. Brian Silverman who gave me permission to publish it.

I noticed that you were asking for interesting factoids about the number 11.

This isn't quite a factoid about 11 but here's a math puzzle a Russian friend of mine said her son worked out with 7th graders. Seems to me to be beyond most undergrads here. I'm not including the answer, to give you a chance to work on it if you want. but will send it if you ask.

"The question is if it's true that among the numbers consisting of only "1"s (1; 11; 111; 1,111; etc.) there is a number (maybe many) that is divisible by 572,003?

Actually, 572003 is taken arbitrarily. 57 is the number of the school (schools here are mostly numbered instead of having names) and 2003 you possibly know what is recently used for (yes, yes, here in Moscow, too). "

Brian

This puzzle doesn't seem at all obvious to me, especially if one needs to solve it for arbitrary numbers other than 572003. I thought of putting it into my pile of problems to someday solve but then thought it'd be fun to post here.

Can Russian 7th graders solve this? How much help did they get?

Can you solve it?

## A great triangle exploration

Mr. Honner has a great exploration at his blog. It starts with a simple question, that has subtlety and depth to it: How do you determine the "equilateralness" of a triangle? Can you compare two triangles and determine which is more equilateral than the other?

The post introducing the investigation is here. I encourage you to do your own exploring before reading the 28 comments which are rich in ideas. Once you've played around with the ideas yourself then take a look at what Mr. Honner came up with in Part II.

I love this kind of exploration for a number of reasons:

- The question is simple to understand.
- Just like in the real world there are multiple approaches.
- It's not clear that there is a right solution but some are better than others.
- Students get to think about properties of triangles in new and different ways.
- Students get to think deeply about the notion of "metric."
- This problem is more interesting than many other geometry problems I've seen.

Nice!

## Seeking interesting math factoids about the number 11

I'll be doing a brief talk at a conference next month, on 11/11/11 at 11:11AM, about the number 11. If you know interesting factoids about 11 (or about 1111...) that I could include in the talk I'd greatly appreciate it.

One factoid is that 1/(1+(1/(1+1/(1+... converges to the golden ratio.

Another is that if a number is divisible by 11, reversing its digits will result in another multiple of 11.

Other ideas?

Thanks.

## Check out “A Cultural Paradox: Fun in Mathematics”

A while back I received this email from Jeff Zilahy.

Dear Mr. Lederman,

I came across your blog, Wild about Math, and I too share your enthusiasm for the world of mathematics. In fact, I wrote a popular math book last year that I wanted to bring to your attention. It is called "A Cultural Paradox: Fun in Mathematics". While you can always purchase it at places like Amazon.com, you can also read the entire book for free (and download the PDF if you like) at Google Books. All I ask if you read it and like it to please write me a review. I am a high school math teacher in Philadelphia and I want to write another book so every review counts!

Thanks in advance,

Jeff

Here's Jeff's introduction to his book.

Do you think "math = awesome" is a true statement? After reading this book, you might change your answer to a yes. With "jargon avoidance" in mind, this recreational math book gives you the lowdown on why math is fun, interesting and relevant in today's society. Intended for anyone who is curious about math and where it is circa 2010. This book is less concerned with exploring the mathematical details than it is with exploring the overall impact of various discoveries and insights, and aims to be insightful, cutting edge-y and mathematically rigorous.

"A Cultural Paradox: Fun in Mathematics" is a fun, light and quick read. It's a nice book for a young person who enjoys Math or science. It appeals to our natural sense of curiosity about math and numbers through enjoyable little stories.

Jeff's book is indeed available at Google Books here. You can buy it as a Google Ebook for $1.99 USD or you can download the PDF for free from this page. Click on the "PDF" link to download the book. And, leave Jeff a review.

## Bad pun

From the great Math humor blog, Patrick at Math Joke 4 Mathy Folks, writes:

Feeling a little hungry, f(x) = x^2 + 3 walks into a restaurant. “Got any sandwiches?” he asks.

“Sorry,” says the waiter, “we don’t do catering for functions.”

## Stephen Wolfram on Steve Jobs and his influence on Mathematica

Stephen Wolfram wrote a nice article on his personal blog: Steve Jobs: A Few Memories.

## Real-world math activities at yummymath.com

[ *Editor's note: Brian at Yummymath contacted me on twitter to introduce me to his web-site. I hadn't heard about it so I went to check it out. I liked what I saw and I offered to promote the site if he wrote a guest article. Here's the guest article.* ]

## Making Math Meaningful to Students: www.yummymath.com

Have you ever heard math students ask “Why do we need to learn this?” or “When am I ever going to use this?” There is a relatively new website, www.yummymath.com whose purpose is to help educators answer those exact questions. The website provides authentic and timely math activities that relate to real life happenings. Math activities are written

about current events that are of interest to students, including sports, technology, movies,

big news stories and holidays. While the activities are written about topics that kids can

relate to, the activities focus on number sense reasoning, problem solving and conceptual

development of math concepts.

Yummymath activities incorporate real life data. For example, a recent activity was

written about the NFL to coincide with the start of the NFL season. The activity was

centered on actual NFL team values, something that is relevant to many students. The

activity represented actual NFL franchise values in bar graph form and focused on

visualizing the concept of the mean. Other notable recent activities include an analysis of

the Harry Potter movie franchise, which coincided with the final Harry Potter movie, and

a “hurricane math” activity that coincided with Hurricane Irene.