Firstly, the phrase "weird" I use is for problems that have a solution where you can't really prove the time complexity with real proof but rather with intuition, estimation... For example problem 2284C2, (I'm not sure if there's any other ways to solve but after my random guess during the contest which got AC and according to many sources) the solution for k = 2 is to brute force to find the value c that gcd(a, c) = gcd(b, c) = 1. It is said that c will be found after approximately 300 steps which I have no idea why. Can anyone explain the boundary 300 steps in the problem and are there any tips to recognize and solve these weird problems?

This is my first time learning competitive coding and I'm really confused about where do I start. Some people say new problems tend to focus on thinking rather than coding while older problems focused on coding, data structures, techniques... Both sound useful but I still can't decide which one to focus on since I don't know which type of problems will be useful for my future.