Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

2022 SSMO Relay Round 1 Problems

Problem 1

Suppose $a, b, c$ are distinct digits where $a \not= 0$ such that $\left(\overline{abc}\right)^2 = \overline{bad00}$ where $d = a+b$. Find $a+2b$.

Solution

Problem 2

Let $T=$ TNYWR. Now, let $\ell$ and $m$ have equations $y=(2+\sqrt{3})x+16$ and $y=\frac{x\sqrt{3}}{3}+20,$ respectively. Suppose that $A$ is a point on $\ell,$ such that the shortest distance from $A$ to $m$ is $T$. Given that $O$ is a point on $m$ such that $\overline{AO}\perp m,$ and $P$ is a point on $\ell$ such that $PO\perp \ell$, find $PO^2.$

Solution

Problem 3

Let $T=$ TNYWR. Now, let $ABC$ a triangle such that $AB=T,$ $AC=100$, and $\angle{ABC}=36^{\circ}.$ Find the remainder when the product of all possible values of $BC$ is divided by $1000$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_SSMO_Relay_Round_1_Problems&oldid=193775"