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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
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Heads or Tails?
nellis25   81
N Yesterday at 9:34 PM by MercuryM
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]
81 replies
nellis25
Jan 24, 2022
MercuryM
Yesterday at 9:34 PM
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A Domino Problem
nellis25   21
N Yesterday at 8:48 PM by VivaanKam
Can you cover this grid with $1 \times 2$ dominoes, without overlap?

[center]IMAGE[/center]
21 replies
nellis25
Jun 22, 2020
VivaanKam
Yesterday at 8:48 PM
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Ring + Bear + Melon + Candy?
cubingsoda   16
N Mar 19, 2025 by Amazingatmath.com
[center]IMAGE

Ring + Bear + Melon + Candy?
IMAGE

$~~~~~~~~~~~~~~$
16 replies
cubingsoda
Mar 2, 2021
Amazingatmath.com
Mar 19, 2025
J
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Matching Cards
nellis25   9
N Mar 13, 2025 by srg2015
Two shuffled standard 52-card decks are placed side-by-side.

What is the reciprocal of the probability that at least one card is in the same position in both decks, to nine decimal places?

[center]IMAGE[/center]
9 replies
nellis25
Jan 17, 2022
srg2015
Mar 13, 2025
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Brain Breaker
nellis25   18
N Mar 11, 2025 by CJB19
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]
18 replies
nellis25
Jul 26, 2021
CJB19
Mar 11, 2025
J
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The Honest Coin Flip
nellis25   46
N Mar 11, 2025 by karthi_pal
You and your friend have agreed to a large wager, which is to be settled by a coin flip. The problem is, you and your friend live in different cities. Your friend could flip a coin and tell you the result by phone, but since the stakes are so high, you don't trust your friend to give a truthful result. (Similarly, you could flip a coin, but your friend doesn't trust you!) Is there a way to flip a coin (or something equivalent) that both of you could trust?

[center]IMAGE[/center]
46 replies
nellis25
Sep 21, 2020
karthi_pal
Mar 11, 2025
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Tough Value
nellis25   5
N Mar 11, 2025 by karthi_pal
What is the value of the following expression? $$\frac{1}{\sqrt{1+ \frac{1}{999^2} + \frac{1}{1000^2}}-1}$$
5 replies
nellis25
Oct 4, 2021
karthi_pal
Mar 11, 2025
J
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Base Bedlam
nellis25   18
N Mar 11, 2025 by Yiyj1
For which positive integers n is the following equation true in base n?

$10^2 + 11^2 + 110^2 = 111^2$

[center]IMAGE[/center]
18 replies
nellis25
Jan 11, 2022
Yiyj1
Mar 11, 2025
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Tryptophan
nellis25   15
N Mar 11, 2025 by mathxqq
After eating too much turkey, Alex, Winnie, and Lizzie got very sleepy. They all fell asleep at exactly 8:00pm and have the following sleep patterns:
[list]
[*] Lizzie sleeps for 5 hours at a time, wakes up, then immediately falls back asleep.
[*] Winnie sleeps for 4 hours at a time, wakes up, then immediately falls back asleep.
[*] Alex sleeps for 3 hours at a time, wakes up, then immediately falls back asleep.
[/list]
The little monsters will all get up if they all happen to wake up at the same time. What time will it be when the three little monsters get up?

[center]IMAGE[/center]
15 replies
nellis25
Nov 23, 2020
mathxqq
Mar 11, 2025
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Every Day I'm Subtractin'
nellis25   14
N Mar 9, 2025 by vishwakarmayojana
Pick a 3-digit number. Make the largest and smallest number you can from its digits. Then find the difference of these two numbers. Using this difference as the next 3-digit number, repeat this process.

For example, starting with 619, we first make 961 and 169, so we get the difference 961 - 169 = 792. Then, from 792, we make 972 and 279, recording the difference 972 - 279 = 693. We would then continue with 693, etc.

What happens in the end? Share your results here!

[center]IMAGE[/center]
14 replies
nellis25
Sep 14, 2020
vishwakarmayojana
Mar 9, 2025
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A Power Tower
nellis25   2
N Jul 31, 2021 by V0305
What is the smallest positive integer $n$ such that

[center]IMAGE[/center]
2 replies
nellis25
Mar 30, 2021
V0305
Jul 31, 2021
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A Power Tower
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nellis25
279 posts
nellis25
#1 h  Mar 30, 2021, 9:28 PM • 1 Y
Y by Mango247
What is the smallest positive integer $n$ such that
https://data.artofproblemsolving.com/images/keeplearning/Week%2052_Website_2_Power%20Tower.png
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RedPenMan
6 posts
RedPenMan
#2 h  Mar 31, 2021, 9:07 PM
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V0305
661 posts
V0305
#3 h  Jul 31, 2021, 1:58 PM
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