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 AIME I Problems/Problem 4

Revision as of 16:34, 17 February 2022 by Bluesoul (talk | contribs)

solution 1

Write $i=e^{i\frac{\pi}{2}}$, it turns to: $\frac{\pi}{6}(3+r)=\frac{4n\pi}{6}$, so $3+r=4s+12k$

it follows a pattern that $s=1,r=1,13....97$ has 9 values; $s=2,r=5,17...89$ 8 values and $s=3,r=9,21,...93$ 8 values.

So the answer is $33*(9+8+8)+9=834$

~bluesoul

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_AIME_I_Problems/Problem_4&oldid=171133"