Here is what I post as an answer sometimes, if I see a question quickly enough for it to make the slightest difference. I have learned to post it CW and not to reply to comments, the people who want help here for these questions want what they want and are unpleasant. Meanwhile, one may claim separation of church and state, nothing I can do about that, but hk was angry that kids were cheating his site; I can see that, on the PE forum's own public Meta, he did use the word embarrassing. His letter is stronger.
Still me: what I see is this Colin Hughes putting in an incredible amount of effort to give students (who may not have done well in a traditional class/homework/test environment) an opportunity to learn by doing, using computer programming, something they may find more natural than mathematics. From the magazine article, it is clear that some see this as a way to learn or improve programming instead. The setup is a community intended to be self contained; wide dissemination of answers for the problems undermines the process.
Magazine article by James Sommers :
discussion on MO:
discussion at Project Euler's own forum:
email letter from "hk", Novemeber 2011
let me introduce myself to you. I'm hk at Project Euler.
The philosophy of Colin Hughes, the founder of Project Euler was the philosophy of inductive self learning.
Just Googling on the subject will reveal you quite a lot about this educational subject.
(The top item on my version of Google was this one: http://mate.calpoly.edu/media/files/Review_inductive_learning.pdf)
My personal view on this matter is: if you lack the attitude, when faced with a new problem, to break it down into smaller parts or to
investigate smaller cases you will never never become a successful scientist or academically schooled person.
The problem in question that raised attention to Project Euler is particularly fit for scaling down and discover some useful facts.
I think we are facing a cultural clash here:
The rationalisations shown to us by e.g. rbharvs are from the level: I have to be told how to do things.
I'm afraid that has to do with a failing educational system that shows students rules and formulas without giving them enough room to
experiment before formalising knowledge.
To do some work that is new to you, be it research mathematics or toying around with problems for which all underlying maths is known, you will
need to doodle around with the problem or parts of it. How else can one do essentially new work?
Top down teaching that doesn't help their students to develop this kind of ability produces people that start shouting: tell me how to do it
and I will try to copy it. Some people that are badly educated in the way I sketched are just using Project Euler to develop those skills.
I hope that they will benefit from that in their professional life. Some have even indicated that it was Project Euler that ultimately made them decide to choose mathematics for their academic study despite the poor level of the mathematical education in their country.
The people that posed the questions at Math Overflow, in my opinion have shown to lack the mental attitude to do the necessary doodling around. (Take for instance the fact that one of them copied the radius 10^10. Some experimenting would have shown them that ______).
Well, you can consider this private communication as lunch talk if it doesn't interest you, but I hope I gave you some information about the philosophy of Project Euler. Feel free to paraphrase it to your wish when communicating with your colleagues at Math Overflow.
If you like to know more feel free to email me.
Thanks again for the effort you have invested in the case.