Mathematics Magazine Problem 2214 Solution
Rational numbers as repeated averages starting from 0 and 1
In this article, I provide a solution to Mathematics Magazine Problem 2214.
Starting with 0 and 1, the problem asks us to show that every rational number
between them can be constructed in finitely many steps by averaging distinct
numbers already written down.
It's really interesting because I have previously tried to just repeatedly
average numbers together and found that we can get a lot of different values.
This one formalized this process and also showed me we can do it for every rational
between 0 and 1!
Really cool!!!
I hope you enjoyed reading the article
Any feedback is greatly appreciated!