Could you give some examples of problems you really liked?

Russia 2002 Grade 11 #4
USA TSTST 2012 #9

As for easy problems that I really like, look at the entirety of USA HMMT 2012.

But those are more of "legendary problems" (in my opinion); there are lots of problems which are somewhat better than just "nice". The last two years of IMO have had one problem which I very much enjoyed solving during the test.

IMO 2011 had the windmill problem. The fact that the problem is related to halving lines is very motivated, but I think it's still a remarkable relation. I also liked IMO 2012 #3, mainly because I could use LLL on it.

Here's a list of things (probably incomplete) that could make a problem "great":

-Having a step that's extremely hard to directly motivate. Sadly, currently the ability to use indirect motivation is never taught and never explained. This in turn means that the leaders would never agree to put such a problem on the imo, because only a few people would solve it. But I think the use of indirect motivation to find RIDICULOUS steps is probably the single most fun problem-solving experience.

-A problem on which a very deep understanding of the theory helps.

-A problem that has a ton of freedom that lets it be solved in many different ways.

-A problem that is related to something that seems completely different.

-A problem that seems to lend naturally to generalization and extension.

Etc, etc, etc...

Indonesia first gold medallist ever yay

Indonesia first gold medallist ever yay