Many, not to say most, include forensic science. However, there were and still are some shows, films and film made for television, whose lead characters primarily use their intelligence and their logic, although they are few in numbers.
One good example is the television show, called Murder, She Wrote. This show aired in 1984 and ended in 1996. It starred the British actress, Angela Lansbury. In this show, Angela Lansbury played the English teacher, turned mystery writer, Jessica Fletcher, who is also referred to as J.B. Fletcher (Jessica Beatrice).
In each episode, Jessica Fletcher must solve a murder, with the help of police officers, doctors, and such. Although at times she has access to police records, J.B. Fletcher essentially uses her intelligence, her knowledge, and her logic. She tries to put the different pieces together, in order to discover the identity of the murderer, before he, she or they have a chance to get away with their crime(s).
It is true that the lead character isn't young in age, but don't let that fool you. Jessica Fletcher is a smart old lady, who is very nosy, and she knows how to get what she needs to solve the murder. She has what it takes to solve the crime. At times, it has lead her into serious trouble, but that simply shows her that she is on the right track to finding the murderer or murderers.
Each episode has an interesting twist and ending to it. What is enjoyable is that the clues are there, within the story. The writers made sure of that. And so the audience can try to solve the cases, along side Angela Lansbury, as Jessica Fletcher. All the clues that the detectives and the audience needs are there. All the audience needs to do is to pay close attention and hopefully pick up one or two clues, which will lead them to the murderer's identity or murderers' identities. Some of the clues aren't very obvious, which is why the audience may feel the need to pay close attention.
Keep that in mind and enjoy the show!