🦫 Upstate NY Math Team: Sunday AMC problems

Nov 20, 2024

Upstate New York Math Team

Mathematical Problem Solving

Dear Upstate New York Math Team,

We’ll continue our problem review this Sunday by focusing our attention on some recent AMC 10/12 contest problems. Join us on Sunday November 24 at 9am on Zoom: (https://bard.zoom.us/j/82682517748?pwd=y9JLpHLkj58ZhysTtIzUtHjWBty1ID.1)

Here are some of the problems that you might see solved this Sunday:

AMC 10B #1 In a long line of people arranged left to right, the 1013th person from the left is also the 1010th person from the right. How many people are in the line?

AMC 12A #9. Let M be the greatest integer such that both M + 1213 and M + 3773 are perfect squares. What is the units digit of M?

AMC 10A #24. A bee is moving in three-dimensional space. A fair six-sided die with faces labeled A⁺, A^-, B⁺, B^-, C⁺, and C^- and is rolled. Suppose the bee occupies the point (a, b, c). If the die shows A⁺, then the bee moves to the point (a+1, b, c) and if the die shows A^- then the bee moves to the point (a-1, b, c). Analogous moves are made with the other four outcomes. Suppose the bee starts at the point (0,0,0) and the die is rolled four times. What is the probability that the bee traverses four distinct edges of some unit cube?

See you on Sunday morning!

Japheth

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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

2024 AMC 10/12 Problem Review

Date: Sunday, November 24, 2024

Time: 9:00am - 10:00am (Just one hour.)

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

Description: Let's take an hour to share solutions with each other. Japheth will host an hours worth of solutions. Let's emphasize clear and insightful solutions that are prepared in advance.

Coming up: Topic-focused practices.

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.