Math Quiz 9

[Caleb Sykes]

Originally Posted by FiMFanatic

That has a clear answer, despite the infinite number of numbers between 0 and 1, as each number only occurs once.

The original question has no proper solution as worded.

However, I do applaud the high level of solutions that were provided - well done.

Each line segment in the problem statement also appears only once. So the two questions are directly comparable.

If you can answer my first question (with calculus if you know any), try this one (again with calculus if you know any):
What is the average x coordinate of all ordered pairs (x,y) within the range 0<x<1 and 0<y<1?

In this scenario, multiple (in fact, uncountably infinite) ordered pairs can contain the same x coordinate, but the statement of the problem is sound.