be the set of positive integers. A function 
satisfies the equation ![\[\underbrace{f(f(\ldots f}_{f(n)\text{ times}}(n)\ldots))=\frac{n^2}{f(f(n))}\]](http://latex.artofproblemsolving.com/2/e/7/2e73ff2f75b103e9d6a4004a42e4ed7f4ee64a67.png)
for all positive integers 
.
.
be an integer. Rowan and Colin play a game on an 
grid of squares, where each square is colored either red or blue. Rowan is allowed to permute the rows of the grid and Colin is allowed to permute the columns. A grid coloring is orderly if: [list] [*]no matter how Rowan permutes the rows of the coloring, Colin can then permute the columns to restore the original grid coloring; and [*]no matter how Colin permutes the columns of the coloring, Rowan can then permute the rows to restore the original grid coloring. [/list] In terms of 
is selected inside acute 
so that 
and 
.
is chosen on ray 
so that 
.
be the midpoint of 
.
is tangent to the circumcircle of triangle 
.
that satisfy![\[
f(x^2-y)+2yf(x)=f(f(x))+f(y)
\]](http://latex.artofproblemsolving.com/f/b/b/fbb693770cd90d8a144026608074122e54da5802.png)
for all 
.
and 
be positive integers. The cells of an 
grid are colored amber and bronze such that there are at least 
amber cells and at least 
bronze cells. Prove that it is possible to choose 
chosen cells lie in the same row or column.
and 
are erected outside an acute triangle 
Suppose that ![\[\angle BC_1C+\angle CA_1A+\angle AB_1B=180^{\circ}.\]](http://latex.artofproblemsolving.com/3/3/7/3378f0c4409d14bc0afddf2616992c13f624be3b.png)
Prove that lines 
and 
are concurrent.
-
of the unit squares silver and the remaining squares gold. Kei then folds the grid in half vertically, forming pairs of overlapping unit squares. Let 
and 
?
of identical dominoes is a maximal grid-aligned configuration on the board if 
dominoes where each domino covers exactly two neighboring squares and the dominoes don't overlap: 
be the number of distinct maximal grid-aligned configurations obtainable from 
Y by blueprimes, Pengu14, Alex-131, Ultroid999OCPN
Registration is open until March 14! Find the form here.
Calling all SoCal high-school math students!
From the University of Southern California, the student-run Southern California Mathematics Competition (SCMC) returns for another year!
Contest info
We plan to hold our Spring 2025 contest on Saturday, 29 March, on USC's University Park Campus. This time we are going to introduce the online version! Competitors not in Socal area could select the online version.
However, the online competition will be considered unofficial; i.e. only onsite, in-person competitors will be eligible for awards, but we might still recognize the top scorers. Online competitors will compete in the Individual Round only. We will send out the Team Round problems after the conclusion of the Individual Round, but we will not be collecting answers to these problems or scoring them.
- The intended target audience for this competition is high-school students, but middle-school students are also welcome to participate!
- As is typical, our competition will feature both individual and team-based components: you may choose to compete individually or as part of a team of 4 students, although we strongly encourage you to compete with a team.
- This year we are going to have one division only. All competitors will compete in a 20-problem, 120-minute individual round with problems on topics in algebra, number theory, combinatorics, and geometry.
- Those competitors on a team will then compete in a 10-problem, 30-minute team round. One or more problems on the team round will feature content covered in a faculty lecture given on the day of the competition.
- Before the awards ceremony, we will have a head-to-head MATHCOUNTS Countdown Round-style contest (just for fun). Top 8 competitors face off head-to-head in single-elimination tournament.
Additionally, you may view samples of our past work here. If you're looking for resources to study, this page may also be of help.
Hope to see you there, and math on!
- Bluesoul, SCMC Competition Design Chair
