🦫 Upstate NY Math Team: CUBRMC results

Japheth Wood

Oct 29, 2024

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Upstate New York Math Team

Mathematical Problem Solving

Dear Upstate New York Math Team,

The 2nd annual Big Red Math Competition at Cornell University was a great way to pass an autumn Saturday engaged in math with fellow high school math students from around New York state and beyond.

Upstate students were abundant! Most competed with their own teams of 5 students, but we did have 3 teams for Upstate New York students without enough fellow students from their own school.

In addition to Math contest problems, CUBRMC features a Chess Tournament, a Puzzle Hunt, a Math Talk by Cornell Math Professor Allen Knutson, and a welcome from Cornell Math Department Chair, Tara Holm.

Would you like to see photos from CUBRMC? We’ve shared some in our Discord Server and on our Instagram page.

Here was my favorite problem from the day, maybe because I was able to solve it!

Individual #2. Two 3x3 squares are placed next to each other so that they share an edge of length 1 as shown in the figure. How many ways can we cover all 18 squares with 2x1 tiles?

Another problem that caught my attention:

Individual #6. Bradley can perform one of two operations on an integer: he can either square it or add 1 to it. If Bradley starts with the integer 1, what is the minimum number of operations that Bradley needs to perform to reach exactly 1000?

And the most unexpected problem:

Proof #4. Let x0, x1, x2, … be a sequence given by x0=0, x1=1, and

for all integers n ≥ 0. Show that all terms of the sequence are integers.

How can taking a square root to get the next term never give us an irrational number!?

We plan to have a CUBRMC 2024 Problem Review in November. Perhaps we’ll find out how to solve these problems and more?

Welcome Back! We are holding our first meeting this Sunday, November 3, for a welcome back and introductory session. Note that we’ve changed the start time to 9am. Coach Villani has offered to review the hardest problems from the 2024 ARML session, problems that few or none of our teammates solved.

See you on Sunday morning,

Japheth

—

Japheth Wood is a coach for the Upstate New York Math Team and also a math professor at Bard College in Annandale-on-Hudson, NY.

^*For our purposes, Upstate New York refers to that part of New York State which lies outside of Long Island and New York City. Are you not an Upstate New Yorker? We welcome you to join us at our training sessions, but can’t invite you to be part of our geographically-defined teams at ARML and other contests.

Upcoming Practices

1. Sunday, November 3, 9:00am, ending by 10:30am: Welcome Back, Introductions, and a review of the hardest problems from the 2024 ARML contest.

Zoom: Click Here (https://bard.zoom.us/j/82682517748?pwd=y9JLpHLkj58ZhysTtIzUtHjWBty1ID.1)

2. Review of CUBRMC 2024 Problems. Details TBA

3. Review of the 2024 AMC 10/12 A & B Problems. (To maintain contest security, we remind all students not to discuss AMC problems until after 8 a.m. Eastern Time the day following the contest.) Details TBA

We hope you will join us!

Reminder: Please get ahold of a copy of Paul Zeitz’s Art and Craft of Problem Solving book, which we will use as a common text this year.

AMC 10/12 and 8

These individual contests come very highly recommended, so make sure to sign up at your school.

AMC 10A and 12A contests: Wednesday, November 6, 2024

AMC 10B and 12B contests: Tuesday, November 12, 2024.

Students do not register directly with the AMC, but arrange to take the AMC contests through their contest manager, typically a math teacher at their school.

Practice old AMC 12 problems on the Art of Problem Solving Wiki!

AMC 12 Archive

Practice old AMC 10 problems on the Art of Problem Solving Wiki!

AMC 10 Archive

We will request your AMC 10/12 scores when you apply to be on the Upstate New York ARML Team.