The newsletter provides information about the Navajo Nation Math Circles project. It discusses the goals and growth of the project since 2012, including numbers of students, teachers, and mathematicians involved. It also announces the premiere of a documentary film about the project. The newsletter is intended to help keep members connected throughout the year. It includes an article reprinted from the NSA website about the positive relationship between the NSA and the project. It poses sample math problems and invites readers to submit solutions and contributions to the next issue.

1. Volume 1, Issue 1 July 2016
NAVAJO MATH CIRCLE NEWS
From the Directors’ Desk
Dear Navajo Math Circles member,
We are very happy to have you in our Math Circles, and hope to share with you the beautiful world
of mathematics.
The Navajo Nation Math Circles project started in 2012. The goal of the project has always been to
bring the spirit of mathematics to the Navajo Nation and to spark interest and joy in problem solving
in the students and teachers who participate. Since 2012, it’s been growing in numbers and
complexity, and at the moment it consists of eight parts:
1. Mathematical visitor program.
2. Baa Hózhó Math summer camp.
3. Math festivals.
4. Student mentoring program.
5. Teacher professional development workshops.
6. Teacher mentoring program.
7. Teacher development program.
8. Teacher-led math circles for students.
Here’s what the project looks like by the numbers:
• More than 40 professional mathematicians from all over US have contributed;
• More than 2000 students on the Navajo Nation have been involved;
• More than 250 teachers have participated.
There is even a documentary about NNMC filmed in 2014 – 2015! It was premiered in January of
this year at the Joint Mathematics Meetings in Seattle, and there have been dozens of screenings
since then, including one at the Navajo Nation Museum in Window Rock, at the National Museum of
Navajo Math Circle News 1
We need your help! This
newsletter needs a new
and better name!
If you have an idea for a
title, please send it to:
tatiana.shubin@sjsu.edu

2. Volume 1, Issue 1 July 2016
Mathematics (MoMath) in New York, and at the NSA Headquarters in Fort Meade, to name just a
few. The PBS broadcasts of the film will start this fall.
This is an inaugural issue of our newsletter, and we hope that this newsletter will help us keep all
members of NNMC together all year round.
Best regards,
NNMC Directors
Happy Accidents, Shared Connections and
the Beauty of Math
(REPRINTED WITH PERMISSION FROM WWW.NSA.GOV, NSA IS ONE OF THE MAJOR SPONSORS OF NNMC PROJECT)
A few years ago, Glenn Lilly, Director of the
National Security Agency's (NSA) Mathematics
Research Group, wound his way through a
cavernous conference center searching for his
designated location. Once he arrived, a soft
voice asked, “Do you know about Navajo Math
Circles?” He responded that he did not, and
that simple question began a great relationship
between two groups, NSA and the Navajo Math
Circles project, each with a profound love of
math.
On Monday, June 6, NSA hosted the owner of
that soft voice, Dr. Tatiana Shubin, co-founder/
co-director of the Navajo Nation Math Circles
Navajo Math Circle News 2
David Auckly
Kansas State
University
Henry Fowler
Diné College
Robert Klein
Ohio
University
Amanda Serenevy
Riverbend
Community Math
Center
Tatiana Shubin
San Jose State
University
Screening of the Navajo Math Circles film

3. Volume 1, Issue 1 July 2016
(NNMC) project. Dr. Shubin, a professor at
San Jose State University, was accompanied
by NNMC co-director Dr. Robert Klein of Ohio
University, film producer/director George
Csicsery, and six students/film subjects from
NNMC math camps. The occasion was an
event featuring a sneak peek of the film
Navajo Math Circles, a documentary of the
project. Prior to the film screening, NSA
briefed the directors and students the
agency's contributions to the Nation's
security.
Math has a strong connection with Navajo
culture, influencing everything from the
beauty of textile patterns to how homes are
constructed. The Navajo love of beauty and
the students' view of the beauty of math are
core themes of the film. In Navajo Nation
Math Circles, Navajo traditions of visual and
tactile learning are used to solve math
problems.
NSA stands as one of the chief contributors
to NNMC, established in 2012. Under the
project, hundreds of Navajo students and
teachers have found themselves at the center
of a lively collaboration with mathematicians
from around the world. Students stay late
after school and assemble over the summer
to study mathematics, using a model called
math circles. NNMC has served 2,000
students and 250 teachers throughout its
existence. Additionally, the program boasts
40 mathematicians including NSA employees,
who volunteer regularly to work with
participants.
Marcus, an NSA employee who visited a
NNMC summer camp, joked, “I have a
degree in mathematics and I didn't correctly
solve some of the problems the students
were given.”
Navajo Math Circle News 3
Baa Hózhó Math Camp 2015
Math Circle
Joint Mathematical Meeting in Seattle 2016

4. Volume 1, Issue 1 July 2016
As Dr. Shubin stated in the film, “Our hope is
that all the kids on the reservation will believe
and see that math is cool.”
During the panel discussion after the
screening, the students addressed the link
between mastering math and navigating life.
“Math helps you learn to solve problems on
your own, which helps with school,” said
NNMC student Natanii.
Another student, Briana, noted, “Math is an
everyday thing.”
“And math is the foundation of anything that you want to do,” echoed Charmayne.
For NSA, the reward for cultivating projects such as NNMC is simple. As Mel, a retired NSA
employee and advocate for the project, stated, “We want math to be accessible to everyone.”
Through agency support of this project, NSA continues its mission to foster diversity, by building a
community of NSA mathematicians and the Navajo Nation. Dr. Klein eloquently summarized, “As
NSA well knows, Native Americans helped tremendously during World War II and the future security
of this nation could rest with the Navajo Nation. So we leave them behind at our own peril.”
Navajo Math Circle News 4
“I've had a great time being able to travel all the way to Baltimore and NYC. It was the
farthest East I have ever been. It was both exciting and thrilling. I enjoyed the
company I was with even more because it's been a while since I've seen any of them.
I'm thankful to everyone who was able to support our trip.” – Charmayne Seaton
“This trip to the East Coast gave me the opportunity to have my first experience flying
on plane, riding on train and subway, being on a motored boat, and lastly in an actual
taxi. There were so many things that awed me, from the beautiful scenery to the
exciting, new foods I got to taste. I enjoyed being around the other mathematicians and
feeling not so far from home. While on this trip, I got to realize that my love for math can
take me places, and not everybody can get as great of an opportunity as I did. This trip
has also give me the courage to go and try new things. I had the most fun within the four
days we were out on the East Coast.” -Irvilinda Bahe
Trip to East Coast 2016
To learn more about NNMC project visit our webpage at https://navajomathcircles.org/
To learn more about NMC film see http://www.zalafilms.com/navajo/

5. Volume 1, Issue 1 July 2016
Problem Corner
Problem 1
In the equation below, replace every * with a single digit, 1 through 9, so that:
(a) all six digits are different;
(b) each fraction is in lowest terms;
(c) the equation is correct.
Bonus: Can you find all possible solutions? How do you know that there are no more solutions?
Problem 2
Each cell of a square contains a digit as shown below.
You can start at any cell of the square and walk into any neighboring (namely, sharing a wall) cell,
but it is not allowed to visit any cell more than once.
Ashly walked through the cells as shown below and wrote down all digits she encountered along the
way, thus getting the number 84937561.
Draw a path which results in the largest possible number.
Bonus: Explain how you know that the number you’ve got is, indeed, the largest.
1 8 4
6 3 9
5 7 2
1 8→ 4↓
6↑ 3↓ ←9
5↑ ←7 2
Navajo Math Circle News 5

6. Volume 1, Issue 1 July 2016
Problem 3
Karlsson-on-the-Roof is a fictional character in a series of children's books created by Swedish
author Astrid Lindgren. Karlsson is a very short, very portly and overconfident man who lives in a
small house hidden behind a chimney on the roof of a very ordinary apartment building, on a very
ordinary street in Stockholm. When Karlsson pushes a button on his stomach, it starts a clever little
motor with a propeller on his back allowing him to fly.
One day, his propeller got really old and needed some repairs. To fix it, Karlsson must have 3 new
blades and 1 small screw. The cost of each blade is 120 kronor, and the cost of a screw is 9 kronor.
Fortunately, each purchase of 250 kronor or more qualifies a buyer for a 20% discount on all
subsequent purchases.
Karlsson has exactly 360 kronor. Will he be able to get all he needs – three blades and a screw?
Navajo Math Circle News 6
We would love to receive your solution(s) for any one of the problems. Official
solutions and best received solutions will be published in the next issue of the
Newsletter. Let us know whether or not you would like your name to be included if
your solution is selected for publication. Send your solutions to
tatiana.shubin@sjsu.edu
Would you like to contribute to the next issue of this Newsletter? We would love to
include your stories, photos, interesting math facts and problems in the next issue.
Please send your contributions to tatiana.shubin@sjsu.edu