Three siblings, Ben, Tom, and Lindy Potter, meet Professor Savant while visiting the zoo one rainy day. On Halloween, Lindy is the only brave one to knock on the spookiest house on the block — which turns out to be the home of Professor Savant. After a second meeting, they begin spending time at the Professor's house, where he introduces them to games of concentration and observation. He reveals that there is a magic land called Whangdoodleland that can only be reached through the imagination, and that he is training them to accompany him there.
Whangdoodleland is the home of the last Whangdoodle that lived in the world. Once the Whangdoodle, and other creatures that are now considered imaginary, lived in our world. However, fearing that people were losing their imaginations, the Whangdoodle created a magic and peaceful world over which he reigns. The professor and the children explore this world.
Each time the children return, they venture farther and farther into Whangdoodleland, intending to reach the palace where the Last Whangdoodle resides. However, the Whangdoodle's Prime Minister, the "Oily Prock", does not want them to disturb His Highness, and sets up a number of traps, both in Whangdoodleland and the real world to prevent this meeting. He enlists the marvelous and funny creatures of the land in his effort, including the High Behind Splintercat, the Sidewinders, the Oinck, the Gazooks, the Tree Squeaks, and the Swamp Gaboons. The children use their imaginations, intelligence, and the friendship of another denizen, the Whiffle Bird, to outwit trap after trap, but can they reach the Whangdoodle's castle?
- Another Dimension
- The Baby of the Bunch: Lindy Potter, the youngest of the three siblings, who also has the most fertile imagination out of the group because of her young age.
- Cats Are Mean: The Splintercat, who initially presents himself as a friend to Lindy, but later turns out to be working for Prock.
- Determinator: Professor Savant has spent years trying to reach Whangdoodleland again, but has remained fervently optimistic that he will one day finally meet the Whangdoodle. Subverted near the end when he reveals to the children that he cannot see the bridge leading to the Whangdoodle's palace, forcing him to give up on his lifelong dream. But eventually double subverted when Lindy convinces the Professor to let her help him cross the bridge, finally allowing him to meet the Whangdoodle face-to-face.
- Eccentric Mentor: Professor Savant.
- Evil Chancellor: The "Oily Prock". Subverted in that he bears no ill will towards the children, but still tries to prevent them from seeing the Whangdoodle on account of his mistrust of humans.
- The Fantastic Trope of Wonderous Titles
- Fictional Color: One of the Whangdoodle's powers is being able to turn into whatever color he wants. When asked which color is hardest to do, he says "flange," which is all of the colors of the rainbow, all at once. He finds flange surprisingly easy to do once he's no longer the last of the Whangdoodles.
- Last of His Kind: The Whangdoodle. At the end of the story, Professor Savant succeeds in creating another (female) Whangdoodle for the Whangdoodle.
- Magical Land: Whangdoodleland, which just happens to be one of last remaining holdouts of imaginary creatures since humanity gave up on "imagination" long ago.
- Magic Feather: Played with. Near the end, Professor Savant admits to the Prock that the magic hats he gave the children to help them enter Whangdoodleland have no actual magic in them and were just a ploy to give the children confidence (which is the real reason, rather than his excuse that he's grown beyond needing one, that he never wore one himself). But then it's suggested that the hats might really be magical after all.
- Meaningful Name: "Savant", meaning "a person of learning, especially one who is versed in literature or science; a person who is considered eminent because of their achievements".
- Real Award, Fictional Character: Professor Savant is said to have been awarded the Nobel Prize for his work in genetics.
- Running Gag: "The Whangdoodle has a sweet tooth, you know."
- Silly Rabbit, Cynicism Is for Losers!
- Sweet Tooth: "The Whangdoodle has a sweet tooth, you know." He eats almost nothing but candy, and one of the most notable fittings on his royal barge is a fully-automatic ice cream sundae dispenser.
- Unusual Euphemism: The Professor has a tendency to say "fiddlesticks" whenever something goes wrong.