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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies

jlacosta

Apr 2, 2025

0 replies

D860 : Flower domino and unconnected

Dattier 4

N 10 minutes ago by Haris1

Source: les dattes à Dattier

Let G be a grid of size m*n.

We have 2 dominoes in flowers and not connected like here
IMAGE
Determine a necessary and sufficient condition on m and n, so that G can be covered with these 2 kinds of dominoes.

4 replies

Dattier

May 26, 2024

Haris1

10 minutes ago

Equal Distances in an Isosceles Setting

mojyla222 3

N 30 minutes ago by sami1618

Source: IDMC 2025 P4

Let $ABC$ be an isosceles triangle with $AB=AC$ . The circle $\omega_1$ , passing through $B$ and $C$ , intersects segment $AB$ at $K\neq B$ . The circle $\omega_2$ is tangent to $BC$ at $B$ and passes through $K$ . Let $M$ and $N$ be the midpoints of segments $AB$ and $AC$ , respectively. The line $MN$ intersects $\omega_1$ and $\omega_2$ at points $P$ and $Q$ , respectively, where $P$ and $Q$ are the intersections closer to $M$ . Prove that $MP=MQ$ .

Proposed by Hooman Fattahi

3 replies

mojyla222

Today at 5:05 AM

sami1618

30 minutes ago

standard Q FE

jasperE3 1

N 34 minutes ago by ErTeeEs06

Source: gghx, p19004309

Find all functions $f:\mathbb Q\to\mathbb Q$ such that for any $x,y\in\mathbb Q$ :
$f(xf(x)+f(x+2y))=f(x)^2+f(y)+y.$

1 reply

jasperE3

4 hours ago

ErTeeEs06

34 minutes ago

Dear Sqing: So Many Inequalities...

hashtagmath 33

N 34 minutes ago by GeoMorocco

I have noticed thousands upon thousands of inequalities that you have posted to HSO and was wondering where you get the inspiration, imagination, and even the validation that such inequalities are true? Also, what do you find particularly appealing and important about specifically inequalities rather than other branches of mathematics? Thank you :)

33 replies