I'd be very interested but wouldn't necessarily take part every month due to time constraints. How big a challenge it is each time and the amount of time given would be deciding factors to whether I join in.
I like the second option too but be careful not to make it too specific - with exactly the same resources and goal, we might all just end up with the same solution.
Something similar to
this would be good (and good practice in case it comes up again!) - but obviously that challenge was designed to be very difficult with the existing resources, to show your understanding of
why it was difficult. A competition would need to be more solvable.