to defend himself.  he had to find a princess.  And he had to save her once he found her.  "It's impossible," he said to the darkness.  "I can't do it."  He stood very still.  "I'll go back," he said.  But he didn't move.  "I have to go back."  He took a step backward.  "But I can't go back.  I don't have a choice.  I have no choice."  He took one step forward.  And then another.  "No choice," his heart beat out to him as he went down the stairs, "no choice, no choice, no choice."

The irony here is that Despereaux does in fact have a choice, and he chooses to save the princess.  Then the ball is set in motion.  Despereaux drops the spool of thread which rolls into a horrid rat who smells soup on Despereaux's whiskers.  In hopes of a meal, this rat leads Despereaux directly to the princess.  The Princess Pea, Roscuro (the kidnapper-rat), and Miggery Sow (the poor, misguided servant girl) are sitting in the dungeon at an impasse until Despereaux's cry of "PRINCESS! ... Princess, I have come to save you!"

Suddenly, the smell of soup on Despereaux's whiskers sparks an epiphany in Roscuro, who realizes he doesn't want to do these bad things, ... he only wants light, ... and soup.  The Princess Pea promises Roscuro soup, ... and that is how they exit the dungeon.

Thus, the phrasing of the question "how does Despereaux solve his problem?" is a bit misleading.  He solves his problem through bravery, but it is a collaboration of bravery and epiphany and even serendipity that leads the reader to resolution.

The Tale of Despereaux, which was written by author Kate DiCamillo and published in 2003, is a children’s story about a brave mouse. Despereaux has many problems in the story, including being different from his family and the rest of the mouse community. These differences result in his incarceration in a dungeon. However, Despereaux’s biggest problem is the love he has for a human, Princess Pea, as mice and humans should not be friendly.

When Despereaux escapes from the dungeon, he learns that Princess Pea has been imprisoned by Roscuro the Rat. Despereaux tells the King that Princess Pea is in the dungeon, but the King does not believe him. Despereaux is determined to rescue the princess himself. Following Despereaux’s rescue of Princess Pea, the pair are able to become very good friends.

There are a number of elements that might be considered the central problem in The Tale of Despereaux. At the most basic level, the mouse that is the title character is faced with the universal problem of appropriate moral, ethical development. For him as mouse, there are specific ways this problem plays out. Despereaux must learn to function effectively as a mouse in a society that often discriminates against mice. For their own protection, mice are expected to hide from humans.

One problem arises when Despereaux breaks that rule and is punished by imprisonment. Solving his problem then requires him to escape from captivity.

A second problem arises from his love for a human woman, by which Despereaux also rejects the limits that are put on mice. To prove his love and loyalty for the princess, he must rescue her as well as himself.

Despereaux uses a combination of skill and self-reliance, but also draws on help from others to solve these specific problems, and in doing so he grows up quite a bit.

The major problem in The Tale of Despereaux is the unfriendly relationship between the mice, the rats and the humans. Roscuro the rat caused the death of the Queen which forced the King to outlaw all rats. During Roscuro’s escape after the death of the Queen, Princess Pea spoke harshly towards the rat and because of this the rat grew to resent the Princess. After these events, Despereaux, the unusual mouse with unusual physical features was born. Despereaux encounters the princess and gets attracted to her. The mouse is sentenced to the dungeons to be eaten by rats because of the relationship with the princess. Later in the story, Despereaux overhears a conversation between Roscuro and Mig, the royal maid charged with delivering food to the dungeon guard, with the intentions of harming the princess. Due to Roscuro’s trickery both Mig and the princess are held captive in the dungeon and Despereaux goes to save them. Despereaux gets an opportunity to kill Roscuro using a needle handed to him by the threadmaster who encouraged him when he was sentenced to the dungeon. The princess asks Despereaux not to kill Roscuro and the story ends with the main characters seated at the banquet hall having soup, in what seems to be a reunion of the mice, rats and humans.

The efforts of Despereaux help in solving the problem between the mice, the rats and the humans.