ka February Highlights and 2025 AoPS Online Class Information
jlacosta0
Feb 2, 2025
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!
2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET
2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET
The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.
Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introductory: Grades 5-10
Prealgebra 1
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10
The game of pool includes balls that fit within a triangular rack as shown:
IMAGE
Seven of the balls are "striped" (not colored with a single color) and eight are "solid" (colored with a single color). Prove that no matter how the balls are arranged in the rack, there must always be a pair of striped balls adjacent to each other.
girls are seated at a round table. Initially one girl holds tokens. Each turn a girl who is holding more than one token passes one token to each of her neighbours.
a.) Show that if , the game must terminate.
b.) Show that if it cannot terminate.
girls are seated at a round table. Initially one girl holds tokens. Each turn a girl who is holding more than one token passes one token to each of her neighbours.
a.) Show that if , the game must terminate.
b.) Show that if it cannot terminate.
Denote the girl originally holding all coins . If , we just remove the girl opposite and consider the girls sitting in a row with A in the center. We use a string to represent the coins in each girl's hand. I'll just write out the numbers to the right of .
We use invariants here. Let the 1994 girls have labels . Assign a weight of to each coin holds. Let start with tokens originally. Notice that in each turn, the sum of the weights is invariant mod . However, in order for the game to terminate, each girl must have 1 token. The sum of the weights in this case is , which is NOT congruent to 0 mod 1994. Hence, the game can never terminate.