The Rule of Three - Lucky survives three attempts on his life by the wicked King (thrown over a cliff, sent to the castle with a letter instructing the Queen to kill him, and being sent to the Griffin's lair).
Philip Jackson (The King) & Pauline Moran (The Queen) later worked together for many years in Agatha Christie's Poirot as Inspector Japp and Miss Lemon.
While the credits claim this story is from an early Russian folk tale, it is actually based on the early German folk tale "The Giant with the Three Golden Hairs" (aka "The Devil with Three Golden Hairs"), collected by the Brothers Grimm, and on two tale types in the Aarne-Thompson-Uther catalog of folklore: #461 "The Hairs from the Devil" and #930 "Prophecy that a Poor Boy Will Marry a Rich Girl".
The source story, "The Giant with the Three Golden Hairs" (Bros. Grimm), was adapted as "Kermit and the Three Golden Nose Hairs" in the book 'Muppets Meet the Classics: Fairy Tales from the Brothers Grimm', written by Erik Forrest Jackson, with Muppet illustrations by Owen Richardson, published by Penguin in 2018.