You know, I grew up thinking that our friends had to be exactly like us in almost every way, if not totally. But as an adult, I realize how that mentality is flawed, and you've addressed it perfectly with this post.
Your friends will not always be what you want them to be at every given time. There will be times when they don't meet your requirements for a certain venture or activity together. The solution is not to keep putting them in a box and expecting them to fit in but to let them live freely and measure up in ways that they can.
I'm glad you eventually found someone at school who could fit into the role of a study partner while you maintained your lovely friendship with Bolu.