>This problem is accessible to anyone who knows basic high school algebra
Are you sure? Spotting the pattern isn't easy and I imagine a lot of high schoolers would give up in frustration while going down wrong roads. A good portion probably wouldn't even write down the numbers without errors. And even if you get past that, most high schoolers don't know how to do/write proofs. I'd be shocked if more than 10% could actually complete all your steps.
With challenging problem solving like that I'm afraid you're going to breed a lot of resentment.
I never said it was easy. In fact, in some sense, the problem is much harder than you might realize at first. This particular rabbit hole goes down very deep.
I am not urging this family of problem on all high school students. Rather, on all prospective high school math teachers. They should be able to communicate the joy of problem solving and discovery to any of their students who show an interest and aptitude -- which means these teachers should have done some of this themselves.
Are you sure? Spotting the pattern isn't easy and I imagine a lot of high schoolers would give up in frustration while going down wrong roads. A good portion probably wouldn't even write down the numbers without errors. And even if you get past that, most high schoolers don't know how to do/write proofs. I'd be shocked if more than 10% could actually complete all your steps.
With challenging problem solving like that I'm afraid you're going to breed a lot of resentment.