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

2025 SSMO Relay Round 3 Problems/Problem 3

Revision as of 11:44, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR.</math> The numbers <math>1</math> and <math>2</math> are written on a board. Every second, if the numbers currently on the board are <math>x<...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $T = TNYWR.$ The numbers $1$ and $2$ are written on a board. Every second, if the numbers currently on the board are $x$ and $y,$ the number $x+y$ is written, and one of $x$ or $y$ is erased. After a finite number of seconds, the larger number on the board is $\left\lfloor\sqrt{T}\right\rfloor$. How many possible values can the smaller number take?

Solution

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2025_SSMO_Relay_Round_3_Problems/Problem_3&oldid=260095"