Dear ,
ARML is just three months away, and our preparations are heating up! We've received many new subscriptions in the past several weeks, so welcome, new readers!
We're in that period between the AMC contests and NYSML, and students are getting focused on the Upstate New York Math Team.
Once again a huge thanks to the Problem Squad; I know you'll enjoy this next installment of practice problems, and will learn something new from a careful reading of solutions to the previous problem set.
Will you be at NYSML? I'd love to meet you in person! Please stop and say hello.
– Japheth Wood
P.S.: As usual, I ask you to share the newsletter sign up form with students, parents, math teachers and math team coaches. The next issue will include the Math Team Application Form, so we especially want to connect with potential team members.
Apply to the Upstate New York Math Team!
The application form will be made available in the next issue. The current draft requests the following information. Preference will be given to applications completed by mid-April, so please start collecting your material now.
Personal Information
First Name, Last Name
Sex/Gender, Age, Grade
T-shirt size
E-mail address, Cell Phone number
School and School Address
Your Math Achievements (We will select team members primarily from math achievements and commitment to be on the team, if selected.)
Recent scores on the AMC 10/12 (2019 and 2020)
Recent NYSML and ARML individual scores (2018 and 2019)
Results on other math contests (AIME, USA(J)MO, etc.)
Your Math League, and a Mathematical Reference
Other math information that you feel is important.
Parent / Guardian Information
Parents' or Guardians' names, emails and telephone numbers.
Food and Diet Preferences (We provide about half of your meals for you while we're away.)
Payment Information (Including financial aid requests.)
Health Concerns
Your Commitment to participate fully, and Parental/Guardian Permission
Arrive at ARML Penn State by the Thursday team dinner, May 28.
All day practice sessions on Friday, May 29.
ARML Competition on Saturday, May 30. Depart.
Problems of the Month - March
Prepared by The Problem Squad (Matthew Babbitt and Brendan Caseria)
Each month we offer a set of problems to help you prepare for ARML. We'll send you the solutions a month later. If you solve a problem and want to share your solution, please email us!
We hope you enjoy these challenge and learn some unexpected mathematics in the process. Solve these with your team or on your own!
NEW! March 2020 Problems
February 2020 Problems
January 2020 Problems
December 2019 Problems
November 2019 Problems
NEW! February 2020 Solutions
January 2020 Solutions
December 2019 Solutions
November 2019 Solutions
Please email us if you have helpful feedback for these problem sets!
Did you know that ARML expects your solution to be in a particular format?
Please read the ARML conventions here: ARML Conventions
Bonus Problem of the Month - February
This month's problem is offered by Jessie Tan, the president of the Cornell Math Club. Thanks Jessie!
Suppose that each of the elementary symmetric polynomials S1, ..., Sn in n given real numbers x1, ..., xn is non-negative. Prove or disprove that each number xi is non-negative.
Definitions: The elementary symmetric polynomial Sk in n variables {x1, …, xn} is the sum of products of the xi, taken k at a time. For example, the elementary symmetric polynomials of three variables {a,b,c} are S1=a+b+c, S2 = ab+ac+bc, and S3 = abc. And the elementary symmetric polynomials in n variables {x1, …, xn} are S1 = x1 + x2 + ⋯ + xn, S2 = x1x2 + x1x3 + ⋯ + xn-1xn, ⋯, and Sn = x1x2⋯xn. (And, of course, "non-negative" means "greater than or equal to zero".)
If you are reading this, and you have a math problem that you want to share, send an email to Matthew Babbitt! Include the problem, an answer, and a full solution to your problem.We will include it in a future newsletter, so the other readers have a chance to try it out.
Solution of the February's Bonus Problem of the Month
This month's problem is offered by Matthew Babbit.
Prove that for any odd positive integer n, n12 − n8 − n4 + 1 is divisible by 29.
Solution: The expression factors as (n8−1)(n4−1) = (n4+1)(n4−1)(n4−1), which further factors as (n4+1)(n2+1)2(n +1)2(n −1)2. Note that each factor is even, which accounts for 7 factors of 2. Also, one of (n +1) and (n −1) is a multiple of 4, which accounts for 2 more factors of 2, a total of at least 9.
If you are reading this, and you have a math problem that you want to share, send an email to Matthew Babbitt! Include the problem, an answer, and a full solution to your problem.We will include it in a future newsletter, so the other readers have a chance to try it out.
We really need a logo. Can you help?
Additionally, we need an attractive t-shirt design.
And better team names than "A", "B", and "C".
Upcoming Contests
To learn what ARML is like, and to be prepared, we recommend looking into other contests in the meantime. Here's a short list of math contest opportunities throughout the year. Some are free, but most charge a reasonable fee or request a donation.
Purple Comet (Online). This team-based competition can be done wherever and whenever teams meet, and is held April 21–30, 2020.
CMIMC (Travel). Held in Pittsburgh PA at Carnegie Mellon University, this competition seems to be a bit closer for those on the western side of New York. Contest date: February 1, 2020.
HMMT Online Tournament. This is an unofficial version of the HMMT February tournament, and so if students are unable to participate at the in-place event, they can simulate the rounds at home (or with their team).
SBIMC. The South Brooklyn Invitational Math Competition is a gentle ARML-style contest.
NYSML coaches have been invited to host/participate in NYSMLSeasonal competitions. These local contests include the NYSMLFall (November 16, 2019–December 8, 2019) and the NYSMLWinter (February 24, 2020–March 8, 2020) events. If you know of a NYSMLSeasonal event, please let us spread the word!
NYSML itself is the New York State Math League. Local leagues lead up to the spring championships, this year on March 28, 2020 in Ithaca. We'll ask Upstate New York Math Team applicants for their individual NYSML scores.
DMI is the Downtown Mathematics Invitational, a December contest at Stuyvesant High School of NYC. For NYC schools only.
EigenTournament runs in March at Stony Brook University.
Do you have a friendly math tournament to recommend to readers of this newsletter? Please send Japheth an email!