The good:

a bit of Students must be allowed to progress as fast as they want. Though not fully as once you're in your stuck for 6 weeks in their rythm. Though there are research projects going on too which helps.
Peer tutoring-like: they seem to pick undergraduate students to serve as supervisors

The bad: everything else. Closed source learning materials + a university-like selection program. Such a waste of efforts that could benefit way more people with more open resources.

meta.mathoverflow.net/questions/4889/request-to-keep-an-eye-out-for-promys-admissions-problems asking to remove PROMYS problems from MathOverflow. And it seems to have been mostly accepted. Newbs. Any maths problem should be allowed to be askeable online. There are no fundamentally new problems, copyright takedown is just silly.

PROMYS Europe (2015-)

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promys-europe.org/

European PROMYS offshoot hosted at the University of Oxford. Started in 2015.

The structure seems to be: come every day for 6 weeks, one problem sheet per day. Go.

Strongly against giving answer to problem sets... sad, as of 2024: promys-europe.org/students/faq (archive):

When do I get the solutions to the problems on the problem sets?
When you discover them for yourself: on your own or collaborating with other students. Returning students and counsellors and faculty will support and encourage you, but not by giving you the answers (hint: they don't even give hints). What PROMYS Europe does is offer you the tools and structure to enable you to be a creative mathematician.

and:

What rules are there at PROMYS Europe?
They're mostly the ones you'd expect: don't do anything dangerous or illegal, don't divide by zero, don't even try to skip Friday Fun, and don't give anyone solutions to the problem sets (though collaboration is definitely OK).

It does not seem to be the case for the American version however after a quick look: promys.org/programs/promys/for-students/faq/. Sad to see.

Also participants are strongly forbidden from sharing the problem sheets with anyone from outside the program. Ciro Santilli asked a participant face to face if he could take a look, but was told that they are not allowed to share it. So it is a very clear and strict order. Truly sad.