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 WSMO Tiebreaker Round Problems

Revision as of 15:15, 2 May 2025 by Pinkpig (talk | contribs) (Created page with "==Problem 1== Find the number of factors of <math>24 ^ {6} - 20 ^ {6}.</math> Solution ==Problem 2== If <math>x^3+y^3=768...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 1

Find the number of factors of $24 ^ {6} - 20 ^ {6}.$

Solution

Problem 2

If $x^3+y^3=76895, x<y$ and $x+y=65,$ find $xy.$

Solution

Problem 3

Let $S$ be the set of all values of $a$ such that the area of a triangle with side lengths $5, 7, a$ is a positive integer. Find $\sum_{x\in S}\left(x^2\right).$

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2023_WSMO_Tiebreaker_Round_Problems&oldid=247842"