Art of Problem Solving

Math texts, online classes, and more
for students in grades 5-12.

Visit AoPS Online ‚

Books for Grades 5-12 Online Courses

Engaging math books and online learning
for students ages 6-13.

Visit Beast Academy ‚

Books for Ages 6-13 Beast Academy Online

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

Sign In

Register

Class Schedule Recommendations Olympiad Courses Free Sessions

AoPS Curriculum Beast Academy Online Books Recommendations Other Books & Gear All Products Gift Certificates

Forums Contests Search Help

math training & tools Alcumus Videos For the Win! MATHCOUNTS Trainer AoPS Practice Contests AoPS Wiki LaTeX TeXeR MIT PRIMES/CrowdMath Keep Learning

contests on aops AMC MATHCOUNTS Other Contests

news and information AoPS Blog Emergency Homeschool Resources Podcast: Raising Problem Solvers

just for fun Reaper Greed Control All Ten

view all 0

Sign In

Register

Resources Aops Wiki Login required

Page

FileDiscussionView sourceHistory

Toolbox

Recent changesRandom pageHelpSpecial pages

Search

Login required

Please log in to edit pages.

Return to File:Markov Chain Frog AIME copy.png.

Retrieved from "https://artofproblemsolving.com/wiki/index.php/File:Markov_Chain_Frog_AIME_copy.png"

Art of Problem Solving is an
ACS WASC Accredited School

aops programs

About

Site Info

follow us

Subscribe for news and updates

© 2024 AoPS Incorporated

© 2024 Art of Problem Solving

About Us • Contact Us • Terms • Privacy

Copyright © 2024 Art of Problem Solving

Something appears to not have loaded correctly.

Click to refresh.