What was Jonas' problem in The Giver and how did he solve it?
Jonas lives in a community that is believed to be "perfect," meaning that there is no war, pain, sadness, anger, etc. In order to achieve this "perfection," his community has "forgotten" any memories of anything considered harmful to living a perfect life, and placed the burden of all of its history on the shoulders of one person, "The Receiver." By taking all of the memories of the community, the Receiver enables the people to live a peaceful existence. However, by doing so, the community has also lost all abilities to experience true emotions, including the good ones. It has also lost the ability to grow, change, and become better. It has been devoid of the richness of life for so long that the people have lost the ability to even see color or hear music. Essentially, the people have lost all freedom to be unique and truly happy, but they don't even realize it.
As the new Receiver, Jonas learns all of this, and realizes how poor of an existence his community is living. He realizes what is missing from their lives. His "problem" is that his community is missing out on real life.
After learning that a previous Receiver ran away and let some of the "memories" escape into the community, Jonas decides to do the same thing, so that his community can find true emotion again. He runs away from home to save his community. That is how he solves the problem.