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

1991 OIM Problems/Problem 3

Revision as of 12:48, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>f</math> be an increasing function defined for every real number <math>x</math>, <math>0 \le x \le 1</math>, such that: a. <math>f(0) = 0</math> b. <...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Let $f$ be an increasing function defined for every real number $x$, $0 \le x \le 1$, such that:

a. $f(0) = 0$

b. $f(x/3) = f(x)/2$

c. $f(1-x) = 1 - f(x)$

Find $f(18/1991)$

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

https://www.oma.org.ar/enunciados/ibe6.htm

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1991_OIM_Problems/Problem_3&oldid=207034"