Happy Thanksgiving! Please note that there are no classes November 25th-December 1st.

G
Topic
First Poster
Last Poster
k a AMC 10/12 A&B Coming up Soon!
jlacosta   0
Nov 1, 2024
There is still time to train for the November 6th and November 12th AMC 10A/12A and AMC 10B/12B, respectively! Enroll in our weekend seminars to be held on November 2nd and 3rd (listed below) and you will learn problem strategies, test taking techniques, and be able to take a full practice test! Note that the “B” seminars will have different material from the “A” seminars which were held in October.

[list][*]Special AMC 10 Problem Seminar B
[*]Special AMC 12 Problem Seminar B[/list]
For those who want to take a free practice test before the AMC 10/12 competitions, you can simulate a real competition experience by following this link. As you assess your performance on these exams, be sure to gather data!

[list][*]Which problems did you get right?
[list][*]Was the topic a strength (e.g. number theory, geometry, counting/probability, algebra)?
[*]How did you prepare?
[*]What was your confidence level?[/list]
[*]Which problems did you get wrong?
[list][list][*]Did you make an arithmetic error?
[*]Did you misread the problem?
[*]Did you have the foundational knowledge for the problem?
[*]Which topics require more fluency through practice (e.g. number theory, geometry, counting/probability, algebra)?
[*]Did you run out of time?[/list][/list]
Once you have analyzed the results with the above questions, you will have a plan of attack for future contests! BEST OF LUCK to all competitors at this year’s AMC 10 and AMC 12!

Did you know that the day after both the AMC 10A/12A and AMC 10B/12B you can join a free math jam where our AoPS team will go over the most interesting problems? Find the schedule below under “Mark your calendars”.

Mark your calendars for these upcoming free math jams!
[list][*]November 20th: Amherst College Info Session, 7:30 pm ET: Matt McGann, Dean of Admission and Financial Aid at Amherst College, and Nathan Pflueger, math professor at Amherst College, will host an info session exploring both Amherst College specifically and liberal arts colleges generally. Topics include opportunities in math, the admission process, and financial aid for both US and international students.
[*]November 7th: 2024 AMC 10/12 A Discussion, Thursday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 A, administered November 6. We will discuss some of the most interesting problems from each test!
[*]November 13th: 2024 AMC 10/12 B Discussion, Wednesday, 7:30 pm ET:
[*]AoPS instructors will discuss problems from the AMC 10/12 B, administered November 12. We will discuss some of the most interesting problems from each test![/list]
AoPS Spring classes are open for enrollment. Get a jump on the New Year and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!

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!

Whether you've taken our classes at AoPS Online or AoPS Academies or reached the top echelons of our competition training with our Worldwide Online Olympiad Training (WOOT) program, you can now add your AoPS experience to the education section 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
Sunday, Nov 3 - Mar 9
Tuesday, Nov 5 - Mar 11
Friday, Dec 6 - Apr 4
Sunday, Jan 5 - Apr 20
Wednesday, Jan 15 - Apr 30
Monday, Feb 3 - May 19
Sunday, Mar 2 - Jun 22
Friday, Mar 28 - Jul 18
Sunday, Apr 13 - Aug 10

Prealgebra 1 Self-Paced

Prealgebra 2
Thursday, Nov 7 - Mar 13
Monday, Dec 2 - Mar 31
Wednesday, Jan 8 - Apr 23
Sunday, Jan 19 - May 4 (1:00 - 2:15 pm ET/10:00 - 11:15 am PT)
Monday, Jan 27 - May 12
Tuesday, Jan 28 - May 13 (4:30 - 5:45 pm ET/1:30 - 2:45 pm PT)
Sunday, Feb 16 - Jun 8
Tuesday, Mar 25 - Jul 8
Sunday, Apr 13 - Aug 10

Prealgebra 2 Self-Paced

Introduction to Algebra A
Friday, Nov 8 - Mar 14
Wednesday, Dec 11 - Apr 9
Tuesday, Jan 7 - Apr 22
Wednesday, Jan 29 - May 14
Sunday, Feb 16 - Jun 8 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 23 - Jul 20
Monday, Apr 7 - Jul 28

Introduction to Algebra A Self-Paced

Introduction to Counting & Probability
Thursday, Dec 5 - Mar 6
Wednesday, Jan 8 - Mar 26
Thursday, Jan 30 - Apr 17
Sunday, Feb 9 - Apr 27 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)
Sunday, Mar 16 - Jun 8
Wednesday, Apr 16 - Jul 2

Introduction to Counting & Probability Self-Paced

Introduction to Number Theory
Monday, Dec 2 - Mar 3
Tuesday, Jan 28 - Apr 15
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3

Introduction to Algebra B
Wednesday, Dec 11 - Apr 9
Tuesday, Jan 28 - May 13
Thursday, Feb 13 - May 29
Sunday, Mar 2 - Jun 22
Monday, Mar 17 - Jul 7
Wednesday, Apr 16 - Jul 30

Introduction to Geometry
Monday, Nov 11 - May 12
Wednesday, Nov 13 - May 14 (9:30 - 11:00 pm ET/6:30 - 8:00 pm PT)
Tuesday, Dec 10 - Jun 3
Wednesday, Jan 8 - Jun 18
Thursday, Jan 30 - Jul 10
Friday, Feb 14 - Aug 1
Tuesday, Mar 4 - Aug 12
Sunday, Mar 23 - Sep 21
Wednesday, Apr 23 - Oct 1

Paradoxes and Infinity
Sat & Sun, Nov 16 - Nov 17 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Nov 10 - May 11
Tuesday, Dec 3 - May 27
Friday, Jan 17 - Jun 27
Wednesday, Feb 12 - Jul 23
Sunday, Mar 16 - Sep 14
Tuesday, Mar 25 - Sep 2
Monday, Apr 21 - Oct 13

Intermediate Counting & Probability
Thursday, Nov 7 - Mar 27
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3

Intermediate Number Theory
Thursday, Feb 20 - May 8
Friday, Apr 11 - Jun 27

Precalculus
Sunday, Nov 10 - Apr 27
Tuesday, Dec 10 - May 20
Wednesday, Jan 8 - Jun 4
Tuesday, Feb 25 - Jul 22
Sunday, Mar 16 - Aug 24
Wednesday, Apr 9 - Sep 3

Advanced: Grades 9-12

Olympiad Geometry
Wednesday, Mar 5 - May 21

Calculus
Tuesday, Dec 10 - Jun 10
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Mon, Wed & Fri, Dec 2 - Jan 10 (meets three times each week!)
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2

MATHCOUNTS/AMC 8 Advanced
Tuesday, Nov 5 - Feb 11
Mon, Wed & Fri, Dec 2 - Jan 10 (meets three times each week!)
Tue, Thurs & Sun, Dec 10 - Jan 19 (meets three times each week!)
Sunday, Feb 16 - May 4
Friday, Apr 11 - Jun 27

Special AMC 8 Problem Seminar A
Sat & Sun, Jan 11 - Jan 12 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

Special AMC 8 Problem Seminar B
Sat & Sun, Jan 18 - Jan 19 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

AMC 10 Problem Series
Sunday, Feb 9 - Apr 27
Tuesday, Mar 4 - May 20
Monday, Mar 31 - Jun 23

AMC 10 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)

Special AMC 10 Problem Seminar B
Sat & Sun, Nov 2 - Nov 3 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

AMC 12 Problem Series
Sunday, Feb 23 - May 11

AMC 12 Final Fives
Sunday, Feb 9 - Mar 2 (3:30 - 5:00 pm ET/12:30 - 2:00 pm PT)

Special AMC 12 Problem Seminar B
Sat & Sun, Nov 2 - Nov 3 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

AIME Problem Series A
Tue, Thurs & Sun, Jan 7 - Feb (meets three times each week!)

AIME Problem Series B
Mon, Wed & Fri, Jan 6 - Jan 31 (meets three times each week!)

Special AIME Problem Seminar A
Sat & Sun, Jan 25 - Jan 26 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

Special AIME Problem Seminar B
Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

F=ma Problem Series
Wednesday, Feb 19 - May 7

Programming

Introduction to Programming with Python
Monday, Dec 2 - Mar 3
Friday, Jan 17 - Apr 4
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16

Intermediate Programming with Python
Tuesday, Feb 25 - May 13

Science

Introduction to Physics
Tuesday, Dec 10 - Mar 11
Friday, Feb 7 - Apr 25
Sunday, Mar 30 - Jun 22

Physics 1: Mechanics
Sunday, Feb 9 - Aug 3
Tuesday, Mar 25 - Sep 2

Relativity
Sat & Sun, Dec 14 - Dec 15 (4:00 - 7:00 pm ET/1:00 - 4:00pm PT)
0 replies
jlacosta
Nov 1, 2024
0 replies
Nordic squares!
mathisreaI   35
N 10 minutes ago by YaoAOPS
Source: IMO 2022 Problem 6
Let $n$ be a positive integer. A Nordic square is an $n \times n$ board containing all the integers from $1$ to $n^2$ so that each cell contains exactly one number. Two different cells are considered adjacent if they share a common side. Every cell that is adjacent only to cells containing larger numbers is called a valley. An uphill path is a sequence of one or more cells such that:

(i) the first cell in the sequence is a valley,

(ii) each subsequent cell in the sequence is adjacent to the previous cell, and

(iii) the numbers written in the cells in the sequence are in increasing order.

Find, as a function of $n$, the smallest possible total number of uphill paths in a Nordic square.

Author: Nikola Petrović
35 replies
1 viewing
mathisreaI
Jul 13, 2022
YaoAOPS
10 minutes ago
The straight lines converge on the tangent
cuden   3
N 24 minutes ago by vsarg
Problem: Given an inscribed triangle ABC (O) with Euler center N and Feuerbach point F_e. X,Y,Z are the adjacent Feuerbach points. The tangent line at X of (N) cuts BC at D. Similarly, we have points E,F. EF intersects YZ at P. Define the same points Q and R. Prove that the three lines DP, FQ, ER are concurrent at T and TF_e touches (I)

(Sorry for this ugly drawing :( :( )
3 replies
1 viewing
cuden
Sunday at 1:59 PM
vsarg
24 minutes ago
Polynomial problems
Nomad_from_QZ   2
N 36 minutes ago by Nomad_from_QZ
Find all polynomials p(x) for real x: p(x+p(x))=x²p(x)
2 replies
Nomad_from_QZ
an hour ago
Nomad_from_QZ
36 minutes ago
Coincidence of concurrency points
aZpElr68Cb51U51qy9OM   18
N 36 minutes ago by Mathandski
Source: Sharygin First Round 2013, Problem 19
a) The incircle of a triangle $ABC$ touches $AC$ and $AB$ at points $B_0$ and $C_0$ respectively. The bisectors of angles $B$ and $C$ meet the perpendicular bisector to the bisector $AL$ in points $Q$ and $P$ respectively. Prove that the lines $PC_0, QB_0$ and $BC$ concur.

b) Let $AL$ be the bisector of a triangle $ABC$. Points $O_1$ and $O_2$ are the circumcenters of triangles $ABL$ and $ACL$ respectively. Points $B_1$ and $C_1$ are the projections of $C$ and $B$ to the bisectors of angles $B$ and $C$ respectively. Prove that the lines $O_1C_1, O_2B_1,$ and $BC$ concur.

c) Prove that the two points obtained in pp. a) and b) coincide.
18 replies
aZpElr68Cb51U51qy9OM
Apr 8, 2013
Mathandski
36 minutes ago
No more topics!
A colouring game on a grid
Tintarn   0
Nov 16, 2024
Source: Baltic Way 2024, Problem 8
Let $a$, $b$, $n$ be positive integers such that $a + b \leq n^2$. Alice and Bob play a game on an (initially uncoloured) $n\times n$ grid as follows:
- First, Alice paints $a$ cells green.
- Then, Bob paints $b$ other (i.e.uncoloured) cells blue.
Alice wins if she can find a path of non-blue cells starting with the bottom left cell and ending with the top right cell (where a path is a sequence of cells such that any two consecutive ones have a common side), otherwise Bob wins. Determine, in terms of $a$, $b$ and $n$, who has a winning strategy.
0 replies
Tintarn
Nov 16, 2024
0 replies
A colouring game on a grid
G H J
Source: Baltic Way 2024, Problem 8
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Tintarn
8982 posts
#1
Y by
Let $a$, $b$, $n$ be positive integers such that $a + b \leq n^2$. Alice and Bob play a game on an (initially uncoloured) $n\times n$ grid as follows:
- First, Alice paints $a$ cells green.
- Then, Bob paints $b$ other (i.e.uncoloured) cells blue.
Alice wins if she can find a path of non-blue cells starting with the bottom left cell and ending with the top right cell (where a path is a sequence of cells such that any two consecutive ones have a common side), otherwise Bob wins. Determine, in terms of $a$, $b$ and $n$, who has a winning strategy.
Z K Y
N Quick Reply
G
H
=
a