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

2023 SSMO Relay Round 2 Problems

Problem 1

Consider the cubic polynomial $P(x)=ax^3+bx^2+cx+d$, where $a,b,c,d$ are single-digit integers, which has roots of approximately \[x \approx -0.9518399, 0.2055095, 1.460616.\] Compute $|f(3)|$.

Solution

Problem 2

Let $T=$ TNYWR. Suppose that $L = \left\lfloor\sqrt{N}\right\rfloor$ points are evenly spaced around the circle. Find the number of ways to select $k \ge 3$ points such that the $k$-gon formed strictly contains the center of the circle.

Solution

Problem 3

Let $T=$ TNYWR. In a committee of $2023$ people, $N$ are scientists and the rest are builders. In order to make a building, $\frac{N}{2}$ people must be choosen with at least one scientist and one builder. If $x$ is the number of ways to do this, find the largest integer $a$ such $2^a \mid x$.

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_SSMO_Relay_Round_2_Problems&oldid=207612"