There are several problems and solutions in the book Frindle, but I would surmise that this question is trying to focus on the main problem and solution. The main conflict in Frindle is the man-versus-man conflict that exists between Nick Allen and Mrs. Granger. It is a fairly straightforward power conflict. Mrs. Granger is the teacher. Nick is the student, and Nick refuses to do what Mrs. Granger has asked. Nick has decided to invent a new word, and the word is "frindle." A frindle is a pen, and Mrs. Granger isn't on board with such a nonsensical, made-up word. Nick is frustrated by the response, because the class had previously discussed how words come to be.

"Who says dog means dog? You do, Nicholas. You and I and everyone in this class and this school and this town and this state and this country. We all agree."

If Nick was a student that wanted nothing more than to please his teacher, the frindle idea and word usage would have been dropped immediately after Mrs. Granger expressed her displeasure. But Nick is not that kind of student, and his response is to escalate his attacks on Mrs. Granger's strict classroom order. Nick gets his friends involved, Mrs. Granger gets the principal involved, and Nick's parents become engaged in the conflict. The entire thing spirals out of a control, much to the delight of readers.

This conflict is resolved many years later, when the word "frindle" appears in the dictionary and Mrs. Granger admits to intentionally being Nick's villain and concedes "defeat." Nick realizes that she helped him achieve success and is now letting him know that he did a good thing.

The problem, if you can call it that, which arises in Frindle is that Nick Allen is too creative and too smart to be sitting in a fifth grade language arts class. Nick, known for being smart and rebellious, gets into a conflict with his teacher, the notoriously strict Mrs. Granger. The conflict around the word "frindle" is not the first time our protagonist finds himself in trouble. Having previously decorated a classroom to be a tropical paradise and chirped like a bird to disrupt another class, teachers have come to have eyes in the back of the heads around Nick Allen.

The primary conflict of Frindle—and the problem referred to in your question—arises when Mrs. Granger overhears Nick using the word "frindle" in place of pen. Mrs. Granger bans the word, which, of course, leads to it being used increasingly by many of the kids in Nick's class. The "frindle" controversy soon becomes big enough that the local newspaper pays attention to it, and then it even gets trademarked by a local businessman and picked up by media far more influential than the local newspaper.

The second part of your questions asks about a solution. Well, the need for a solution arises when newfound fame and wealth (in the form of a growing trust fund) start to distress Nick. In an ironic twist, it is Mrs. Granger who counsels Nick and teaches him strategies for living with the heightened attention.

The problem in Andrew Clements' Frindle, also called the conflict, concerns the fact that Nick Allen, the protagonist, is an unusually creative person. As a creative person, Nick has a tendency to do things that are contrary to what the rest of society does, which also means Nick constantly challenges authority in order to express himself. In Frindle, Nick challenges authority by deciding to call a pen a frindle. Since Nick is challenging the rest of society by renaming a pen a frindle, we can call this a character vs. society conflict. However, Nick's decision to call a pen a frindle is opposed most by his third-grade teacher, Mrs. Granger; therefore, we can also call this a character vs. character conflict.

Nick first begins being influenced to invent a new word, such as frindle, when he asks Mrs. Granger who decides what words mean, and she responds with the following answer:

Who says dog means dog? You do, Nicholas. You and I and everyone in this class and this school and this town and this state and this country. We all agree. (p. 28)

Soon after this speech, Nick gets the brainstorm to exercise his authority to decide what words mean by calling a pen a frindle. Yet, Mrs. Granger objects to this decision and fights against it because, for one reason, in her view, the meaning of words are not arbitrary. The meanings of words have extensive background and have already been agreed upon and laid down in the dictionary as law by good authority.

The solution of the story, also called the resolution, occurs when, at the age of 21, Nick's word is added to the dictionary, a symbol that he should continue to be creative and challenge the world, accomplishing great, new things, despite opposition. Furthermore, by the time we reach the end of the story, we learn that Mrs. Granger had only been angry at first. As she explains in the letter she gives Nick at the age of 21, she had come to realize that Nick was doing exactly what every teacher wants students to do: "take an idea they have learned in a boring old classroom and put it to a real test in their own world" (p. 85). In other words, she was proud to see Nick think his own thoughts and run with them, something most people never do. She further explains that the reason why she decided to stick to opposing his idea is because she knew his idea would never take off if he did not have opposition, someone to "be the villain" (p. 85). As Nick explains in his own thoughts after reading the letter, "The old fox! She had been rooting for frindle the whole time. By fighting against it, she had actually helped it along" (p. 86). Hence, the story further resolves once Nick comes to understand how influential he, one small person with creative ideas, can truly be, and realizes just how many people in the world have been rooting for him all along.

What is the solution to the conflict/problem in Andrew Clements' book Frindle?

The conflict in Andrew Clements' book Frindle is solved, or resolves, when Nick comes to understand just how influential he can be by carrying out his creative ideas.

After Nick's accomplishment of inventing a new word and making it popular is reported by the news, Nick's town begins quieting down even though usage of the word frindle remains just as persistent and popular as ever. Regardless of the continued popularity of the word, Nick begins feeling a bit guilty for having caused such a great big ruckus. As the narrator explains, suddenly all of Nick's creative ideas "scared him a little," and Nick became very quiet (p. 76). Mrs. Granger notices his quietness and explains to him that "he didn't do anything wrong" (p. 79). She further explains that she was proud of his "good idea" and of how he handled it and knows he has "great things to do in this life" (p. 79). After this speech, Nick feels encouraged to pursue his next big idea of changing the school's lunch program. He also grows up to pursue college and reaches the age he can legally take possession of the trust fund containing the money he earned from frindle merchandise sales. All of these instances help him see just how powerful his creative ideas can truly be.

However, when he is 21 years old, the moment he fully realizes his power is the moment Mrs. Granger sends him a dictionary containing an entry for his new word frindle. She also sends him the letter she had written him ten years ago explaining she is proud of the change he has made and that she chose to oppose the creation of the new word because she knew opposing it would help increase the chances of it becoming a real word. It is after he reads the dictionary entry and her letter that he fully understands just how much he has the power to change the world and just how much he needs to accomplish great changes in the world.

Hence, the story resolves when Nick fully understands the power of his creativity.