Start the New Year strong with our problem-based courses! Enroll today!

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k a January Highlights and 2025 AoPS Online Class Information
jlacosta   0
Jan 1, 2025
Happy New Year!!! Did you know, 2025 is the first perfect square year that any AoPS student has experienced? The last perfect square year was 1936 and the next one will be 2116! Let’s make it a perfect year all around by tackling new challenges, connecting with more problem-solvers, and staying curious!

We have some fun new things happening at AoPS in 2025 with new courses, such as self-paced Introduction to Algebra B, more coding, more physics, and, well, more!

There are a number of upcoming events, so be sure to mark your calendars for the following:

[list][*]Accelerated AIME Problem Series classes start on January 6th and 7th. These AIME classes will run three times a week throughout the month of January. With this accelerated track, you can fit three months of contest tips and training into four weeks finishing right in time for the AIME I on February 6th.
[*]Join our Math Jam on January 7th to learn about our Spring course options. We'll work through a few sample problems, discuss how the courses work, and answer your questions.
[*]RSVP for our New Year, New Challenges webinar on January 9th. We’ll discuss how you can meet your goals, useful strategies for your problem solving journey, and what classes and resources are available.
Have questions? Our Academic Success team is only an email away, write to us at success@aops.com.[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 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! 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, 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
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
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
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
Tuesday, Jan 28 - Apr 15
Sunday, Feb 16 - May 4
Monday, Mar 17 - Jun 9
Thursday, Apr 17 - Jul 3

Introduction to Algebra B
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
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

Intermediate: Grades 8-12

Intermediate Algebra
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
Monday, Feb 10 - Jun 16
Sunday, Mar 23 - Aug 3

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

Precalculus
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
Friday, Feb 28 - Aug 22
Sunday, Mar 30 - Oct 5

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Tuesday, Feb 4 - Apr 22
Sunday, Mar 23 - Jun 15
Wednesday, Apr 16 - Jul 2

MATHCOUNTS/AMC 8 Advanced
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)

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)

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
Friday, Jan 17 - Apr 4
Sunday, Feb 16 - May 4
Monday, Mar 24 - Jun 16

Intermediate Programming with Python
Tuesday, Feb 25 - May 13

USACO Bronze Problem Series
Sunday, Jan 5 - Mar 23
Thursday, Feb 6 - Apr 24

Physics

Introduction to Physics
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
Jan 1, 2025
0 replies
Heads or Tails?
nellis25   63
N Friday at 2:57 AM by Yiyj1
Winnie keeps flipping a coin until she gets either two heads in a row or three tails in a row, at which point she stops.

What is the probability her final flip is heads?

[center]IMAGE[/center]
63 replies
nellis25
Jan 24, 2022
Yiyj1
Friday at 2:57 AM
Missing Lights
nellis25   30
N Dec 31, 2024 by Even_Lee
There are 8 lights arranged in a circle. Each of them is randomly lit either red, green, or blue.

What is the probability that there are six consecutive lights which are lit up in at most two colors?

[center]IMAGE[/center]
30 replies
nellis25
Jan 24, 2022
Even_Lee
Dec 31, 2024
Clod's Choice Claim
nellis25   7
N Dec 31, 2024 by Even_Lee
Calamitous Clod claims that for a certain choice of two numbers below, the product is nonnegative. Can you certify Clod's claim?

\[ \frac{65523246}{13580164} - 4.8249, \qquad 1.015 - \frac{3^{3^{\log \pi}}}{\pi^3}, \qquad \frac{2^{2^{2^{2^2}}}}{8^{50}} - 1.45 \]
[center]IMAGE[/center]
7 replies
nellis25
Oct 12, 2020
Even_Lee
Dec 31, 2024
The Vexing Hexagon
nellis25   18
N Dec 31, 2024 by Even_Lee
In this regular hexagon, which is greater, purple or orange?

[center]IMAGE[/center]
18 replies
nellis25
Nov 9, 2020
Even_Lee
Dec 31, 2024
Like Twenty-four
nellis25   24
N Dec 31, 2024 by Even_Lee
Using exactly one multiplication, one addition, one division, and one subtraction, what is the smallest positive number you can create using the numbers 4, 5, 6, 7, and 8 once each? For instance, we can form the number ((8÷5) x 7) - (4+6)= 1.2 in this way.

[center]IMAGE[/center]
24 replies
nellis25
Dec 20, 2021
Even_Lee
Dec 31, 2024
MOEMS Style Problem
geobear   13
N Dec 31, 2024 by sinuster
Here's a little MOEMS style problem I made:

Find the probability that the random product $AB$ from the set:

$$A= {1, 3, 5, 7}$$
$$B={2, 4, 6, 8}$$
is divisible by $4.$
13 replies
geobear
Apr 16, 2020
sinuster
Dec 31, 2024
Brain Breaker
nellis25   15
N Dec 24, 2024 by EaZ_Shadow
This multiple choice question has at least one correct answer. If you guessed at random, what is the probability your answer would be incorrect?

\begin{align*}
{\color{blue}{\textrm{A: }}} &\quad 0 &{\color{red}{\textrm{E: }}} &\quad 1/4    \\
{\color{red}{\textrm{B: }}} &\quad 1/4 &{\color{blue}{\textrm{F: }}} &\quad  1/8  \\
{\color{blue}{\textrm{C: }}} &\quad  1/2 &{\color{red}{\textrm{G: }}} &\quad 3/4  \\
{\color{red}{\textrm{D: }}} &\quad 3/4   &{\color{blue}{\textrm{H: }}} &\quad 1 
\end{align*}
[center]IMAGE[/center]
15 replies
nellis25
Jul 26, 2021
EaZ_Shadow
Dec 24, 2024
My Answer...
ChaitraliKA   1
N Dec 22, 2024 by Aaronjudgeisgoat
17×(17+17+17+17+17+17+17)−(17÷17)=2022
1 reply
ChaitraliKA
Jan 30, 2023
Aaronjudgeisgoat
Dec 22, 2024
Cutting a Ring
nellis25   21
N Dec 22, 2024 by DavidLim
What is the maximum number of pieces a ring can be cut into by 3 straight lines? In the example below, the ring is cut into 6 pieces.

[center]IMAGE[/center]
21 replies
nellis25
Jul 6, 2020
DavidLim
Dec 22, 2024
Pie Logic
nellis25   22
N Dec 21, 2024 by Tabhawaii
Six logicians have just finished their Thanksgiving repast, and are ready for dessert. Their host comes around and asks "Would all of you like some pumpkin pie?"

First logician: "I don't know."
Second logician: "I don't know."
Third logician: "I don't know."
Fourth logician: "I don't know."
Fifth logician: "I don't know."
Sixth logician: "No."

Who wants pumpkin pie?

[center]IMAGE[/center]
22 replies
nellis25
Nov 23, 2020
Tabhawaii
Dec 21, 2024
A Riddle from Outer Space
vishwathganesan   5
N Nov 24, 2024 by benryu
Here's an original riddle from three years ago, tweaked a little to be simpler:

On the distant planet of Vukovar, math is done in much the same way as it is here. They even use the same symbols as us, but all of their arithmetic seems to be wrong. Here's a list of equations which are all correct on Vukovar:

$2 + 3 = 6$
$402 + 158 = 671$
$2492 - 651 = 1630$
$7 \cdot 4 = 39$
$35 \cdot 62 = 2247$
$\frac{8029}{139} = 27$
$17 ^ 2 = 10841$

Given this information, what is the value of $(\frac{141}{25}) ^ 3 - (23 \cdot 48 + 74)$ on Vukovar?

Note: This riddle does not require advanced math. A basic knowledge of arithmetic should suffice. Calculators are allowed and could be helpful, but are not necessary.
5 replies
vishwathganesan
Mar 9, 2021
benryu
Nov 24, 2024
A Riddle from Outer Space
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G H BBookmark kLocked kLocked NReply
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vishwathganesan
642 posts
#1
Y by
Here's an original riddle from three years ago, tweaked a little to be simpler:

On the distant planet of Vukovar, math is done in much the same way as it is here. They even use the same symbols as us, but all of their arithmetic seems to be wrong. Here's a list of equations which are all correct on Vukovar:

$2 + 3 = 6$
$402 + 158 = 671$
$2492 - 651 = 1630$
$7 \cdot 4 = 39$
$35 \cdot 62 = 2247$
$\frac{8029}{139} = 27$
$17 ^ 2 = 10841$

Given this information, what is the value of $(\frac{141}{25}) ^ 3 - (23 \cdot 48 + 74)$ on Vukovar?

Note: This riddle does not require advanced math. A basic knowledge of arithmetic should suffice. Calculators are allowed and could be helpful, but are not necessary.
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jasperE3
10967 posts
#2
Y by
It's impossible to make any deduction from the axioms given, since no axioms are given for manipulating equations.
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vishwathganesan
642 posts
#3
Y by
Think of this as a logic puzzle. The goal is not to get an answer which is mathematically guaranteed to be correct, but rather to find an answer which feels satisfying, sort of like those "what comes next in the sequence" problems. And the intended answer is both quite possible to find and should be satisfying to most everyone.
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little_math_monster
10 posts
#4 • 1 Y
Y by aidan0626
Is is this?
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warrending
128 posts
#5
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Hint( I guess):Click to reveal hidden text
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benryu
21 posts
#6
Y by
little_math_monster wrote:
Is is this?

i think is is is
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