Possibly off topic because it's about mathematical community rather than mathematics directly.
Assuming that the answer to Mathematical competitions for adults. is still up to date...
The motivation:
I recently become involved with preparing junior high aged kids for mathletics events. It rekindled my own interest in considering tough problems, so I decided to sit in on a practice session for my local university's Putnam group. I enjoyed that as well.
And now I'm stuck for what to do next.
I do intend to continue my own recreational exploration, and I'm interested in setting up some regular sessions for practicing and collaborating with local problem solvers, but these activities are missing the excitement of the clock and the fun competitive nature of the competitions I wrote as a kid. I'm confident that there are lots of people out there who have as much interest in this sort of thing as myself.
The question(s):
- Why are there no math competitions for unrestricted audiences?
- What makes preparing and administrating contests for students a higher priority than doing the same for general audiences?
- What organizations might take on such a task?
It's part of our culture. By the time we are adults we have made up our mind as to whether we are "good" at math or not. It's no longer seen as something that we can improve at. And with jobs and kids, there isn't that much time to change if we'd like to.
There is nothing stopping you from gathering a group of your friends and finding problems to solve. There are no shortage of textbooks and problem books for you guys to work from. Certainly you can look for inspiration here and on https://matheducators.stackexchange.com/