I always found the Collatz Conjecture to be both simple and fascinating (https://en.wikipedia.org/wiki/Collatz_conjecture)
The operations are understandable to any 9 year old (who won a math competition!), and the implications are far reaching. Additionally, your college winners will understand and appreciate it as well.
It may give the younger ones motivation to think on it (the proof seems it should be sooo simple and yet it's juuuust quite out of reach... for somebody who's just starting in maths; I know I have thought about it a lot when I was young, thinking there MUST have been a simple proof for such as "simple" question).
Lastly, you can always throw in an XKCD for laughs! https://xkcd.com/710/