This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 106

2023 MMATHS, 2
Tags: Yale , MMATHS
The lengths of the altitudes of $\triangle{ABC}$ are the roots of the polynomial $x^3-34x^2+360x-1200.$ Find the area of $\triangle{ABC}.$

2024 MMATHS, 11
Tags: Yale , MMATHS
Let $n$ be the least possible value of $$\sqrt{x^2+y^2-2x+6y+19}+\sqrt{x^2+y^2+8x-4y+21}.$$ Find $n^2.$

2024 MMATHS, 7
Tags: Yale , MMATHS
Bill has the expression $1+2+3+\cdots+8.$ He replaces two different addition symbols with multiplication symbols uniformly at random. The value that he obtains on average can be expressed as a common fraction $\tfrac{m}{n}.$ Find $m+n.$

2021 Girls in Math at Yale, 2
Tags: Yale , college
A box of strawberries, containing $12$ strawberries total, costs $\$ 2$. A box of blueberries, containing $48$ blueberries total, costs $ \$ 3$. Suppose that for $\$ 12$, Sareen can either buy $m$ strawberries total or $n$ blueberries total. Find $n - m$. [i]Proposed by Andrew Wu[/i]

2021 Girls in Math at Yale, 5
Tags: Yale , college
Let $ATHEM$ be a convex pentagon with $AT = 14$, $TH = MA = 20$, $HE = EM = 15$, and $\angle THE = \angle EMA = 90^{\circ}$. Find the area of $ATHEM$. [i]Proposed by Andrew Wu[/i]

2022 Girls in Math at Yale, 6
Tags: Yale , college
Carissa is crossing a very, very, very wide street, and did not properly check both ways before doing so. (Don't be like Carissa!) She initially begins walking at $2$ feet per second. Suddenly, she hears a car approaching, and begins running, eventually making it safely to the other side, half a minute after she began crossing. Given that Carissa always runs $n$ times as fast as she walks and that she spent $n$ times as much time running as she did walking, and given that the street is $260$ feet wide, find Carissa's running speed, in feet per second. [i]Proposed by Andrew Wu[/i]