How to introduce problem solving to primary school pupils? I'm interested into knowing your experiences about introducing problem solving to primary school pupils.

I'm a PhD candidate in Operations Research and, together with my University or my public library, I have organized some laboratories dedicated to problem solving for kids, trying both to entertain children and to make them learn different aspects of mathematics and computer science like they usually see.
Up to now, we have used some puzzles and games (like the 15 puzzle), labyrinths, exercises taken from some local competitions (logical, reasoning, counting, etc.). We have shown them a wide range of topics: sorting algorithms, recursion, very simple automa, trees and family relationships, countings, combinatorial examples, cryptography methods (like Caesar's cipher), etc. The primary goal is to let pupils being fascinated by maths, informatics and their several fields and applications. We would like to increase their creativity, reasoning and modeling abilities.

I have attended some university course about teaching and didactic methods, and now I would like to develop a more structured course, probably focused on one subject than on multiple ones. Beyond the topics, anyway, I kindly ask you to share your experiences, what worked and specially what didn't, speaking in terms of didactics methods.

Thank you in advance.
I have taught problem solving to older learners who studied a range of diagnostic, design and contingency problems. I'm not sure what age group you are talking about which would be handy to know in answering this question.

This is a diagnostic group activity solvable using informal constraint satisfaction.
https://sites.lsa.umich.edu/inclusive-teaching/2017/08/16/who-owns-the-zebra/

Planning activities also work well, surely there will be an end of term party to plan?