In Japan, almost every high school student who wants to enter a college has to take a severe entrance examination. I guess these math problems for the entrance exams are very unique. Because they have to be adequately difficult to select new enrolled college students, but they must not go beyond high school level. That is, they are difficult but they shouldn't require any additional formulas or theorems which are not taught in high schools. Thus, sometimes even university professors fail to solve the entrance exams.
In this page, I can show you some of the math problems which I originally made for high school students for the last couple of years. And some of them were accepted by a monthly published math magazine (which is named "Daigaku eno suugaku" meaning "Math for university"). I made them up on my own, however, I had to make the problems so that they could be solved by high school students, thus it may have been come up with by other persons before. In that case, please email me. Otherwise, I have the copy right.