Advanced Math Puzzles

Warning: these puzzles are so advanced, they'll make you question the very fabric of reality.

Math Puzzle #1: The Infinite Loop

You have a circle with a radius of r. You place a loop within this circle, also with a radius of r. If the loop is perfectly concentric, what is the area of the smaller circle?

Read the solution and see more loop-based puzzles

Math Puzzle #2: The Infinite Recursion

You have a function f(x) that is equal to f(f(x)). If f(x) = x^2 + 1, what is f(5)?

See more recursive puzzles and learn about the dangers of recursive thinking

More puzzles coming soon... or never, depending on how advanced you are.

Explore the theoretical underpinnings of these puzzles or practice your skills with more puzzles