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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
Combinatorial Game
Cats_on_a_computer   2
N 2 minutes ago by Cats_on_a_computer

Let n>1 be odd. A row of n spaces is initially empty. Alice and Bob alternate moves (Alice first); on each turn a player may either
1. Place a stone in any empty space, or
2. Remove a stone from a non-empty space S, then (if they exist) place stones in the nearest empty spaces immediately to the left and to the right of S.

Furthermore, no move may produce a position that has appeared earlier. The player loses when they cannot make a legal move.
Assuming optimal play, which move(s) can Alice make on her first turn?
2 replies
Cats_on_a_computer
16 minutes ago
Cats_on_a_computer
2 minutes ago
2-var inequality
sqing   4
N 6 minutes ago by sqing
Source: Own
Let $ a,b> 0 $ and $2a+2b+ab=5. $ Prove that
$$ \frac{a^2}{b^2}+\frac{1}{a^2}-a^2\geq  1$$$$ \frac{a^3}{b^3}+\frac{1}{a^3}-a^3\geq  1$$
4 replies
sqing
an hour ago
sqing
6 minutes ago
A game of digits and seventh powers
v_Enhance   28
N 12 minutes ago by blueprimes
Source: Taiwan 2014 TST3 Quiz 1, P2
Alice and Bob play the following game. They alternate selecting distinct nonzero digits (from $1$ to $9$) until they have chosen seven such digits, and then consider the resulting seven-digit number by concatenating the digits in the order selected, with the seventh digit appearing last (i.e. $\overline{A_1B_2A_3B_4A_6B_6A_7}$). Alice wins if and only if the resulting number is the last seven decimal digits of some perfect seventh power. Please determine which player has the winning strategy.
28 replies
v_Enhance
Jul 18, 2014
blueprimes
12 minutes ago
n containers distribute gas to a car for a single loop along the track
parmenides51   16
N 22 minutes ago by v_Enhance
Source: Spanish Mathematical Olympiad 1997 P6
The exact quantity of gas needed for a car to complete a single loop around a track is distributed among $n$ containers placed along the track. Prove that there exists a position starting at which the car, beginning with an empty tank of gas, can complete a loop around the track without running out of gas. The tank of gas is assumed to be large enough.
16 replies
+1 w
parmenides51
Jul 31, 2018
v_Enhance
22 minutes ago
No more topics!
nice system of equations
outback   4
N Apr 23, 2025 by Raj_singh1432
Solve in positive numbers the system

$ x_1+\frac{1}{x_2}=4, x_2+\frac{1}{x_3}=1, x_3+\frac{1}{x_4}=4, ..., x_{99}+\frac{1}{x_{100}}=4, x_{100}+\frac{1}{x_1}=1$
4 replies
outback
Oct 8, 2008
Raj_singh1432
Apr 23, 2025
nice system of equations
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G H BBookmark kLocked kLocked NReply
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outback
293 posts
#1 • 2 Y
Y by Adventure10, Mango247
Solve in positive numbers the system

$ x_1+\frac{1}{x_2}=4, x_2+\frac{1}{x_3}=1, x_3+\frac{1}{x_4}=4, ..., x_{99}+\frac{1}{x_{100}}=4, x_{100}+\frac{1}{x_1}=1$
Z K Y
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Bovy11
151 posts
#2 • 3 Y
Y by Adventure10, Mango247, ehuseyinyigit
outback wrote:
Solve in positive numbers the system

$ x_1 + \frac {1}{x_2} = 4, x_2 + \frac {1}{x_3} = 1, x_3 + \frac {1}{x_4} = 4, ..., x_{99} + \frac {1}{x_{100}} = 4, x_{100} + \frac {1}{x_1} = 1$

solution
This post has been edited 2 times. Last edited by Bovy11, Oct 9, 2008, 1:33 PM
Z K Y
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t0rajir0u
12167 posts
#3 • 2 Y
Y by Adventure10, Mango247
Was $ x_{100} + \frac{1}{x_1} = 1$ a typo?
Z K Y
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outback
293 posts
#4 • 2 Y
Y by Adventure10, Mango247
t0rajir0u wrote:
Was $ x_{100} + \frac {1}{x_1} = 1$ a typo?

Why do you think it is?
Z K Y
The post below has been deleted. Click to close.
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Raj_singh1432
3 posts
#5
Y by
t0rajir0u wrote:
Was $ x_{100} + \frac{1}{x_1} = 1$ a typo?

No
Z K Y
N Quick Reply
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