While this might not be a terrific motivator it does have some niceties. Most students will know factorial but will only be able describe it informally - "multiply all the numbers between 1 and n." The recursive definition is more, precise, for lack of a better word.

Then, there's a direct translation between the recursive definition and the code.

Finally, it's about as bare bones as you get - no data structures or undue complexity.

Is this going to motivate a student to learn recursion? No.

Can it be used to help paint a more complete picture? Probably.

Also got a bad rap in the above linked posts. It shares the benefit of the recursive definition directly translating to a coded solution with factorial.

Fibonacci is also a problem where they originally learned it via the recurssive rule "the next Fibonacci number is the sum of the two previous fibonacci numbers."

It also seems that when students find the Fibonacci number problem challenging to solve as beginners without recursion. The whole a becomes b. b becomes c thing can be tricky for beginners. In my experience, they find the recursive solution to be more natural. This is also interesting because they usually don't find recursive factorial more natural than a loop (assuming they learned loops first).

Next, the slowness of the solution is feature, not a bug. It's a platform to talk about how recursion isn't always the answer but you can think about a problem recursively and if the solution isn't right it might lead you to a better solution. This comes up later with dynamic programming. Just last year (he he) during Advent of Code I ended up solving one of the problems via dynamic programming. How did I get there? Thinking about the problem recursively.

Here you get a great platform for now comparing solutions - iterative, recursive, tail recursive, memoization - take it as far as you want.

I can't comment on Euclid's algorithm since I can't recall ever teaching it as part of recursion so I'll substitute Newton's method for square root approximation.

The thing is that here, the goal isn't really recursion. It's just a problem that can be tackled with either recursion or iteration. The reason it's a neat problem is because you can talk about floating point accuracy issues along with how close of an approximation you might want or need.

Finally we get the Towers of Hanoi. Sure it's contrived but it can also be fun and by being a new and different problem students can try to use any strategies that might lead to a solution, recursive or otherwise:

• try some small examples
• see if examples relate to each other
• base case?
• etc.

The big deal though is that Towers of Hanoi isn't really about Towers of Hanoi - it's really a platform to talk about all sorts of good stuff. I wrote all about it a decade ago.

Now, of course you can introduce recursion in other ways particularly if you use a language like Scheme.

Bottom line is that without taking into considerations lots of other factors - student backgrounds, teacher comfort. Time, experience, facilities, goals and desired aoutcomes, and more you can't really say one way is right or one way is wrong.