How do I code the A star algorithm in Scheme?

In the classic science fiction story Now Inhale, by Eric Frank Russell (Astounding Science Fiction April 1959, and in various anthologies), the human hero is a prisoner on a planet where the local custom is to make the prisoner play a game until it is won or lost, and then execution is immediate. The hero is told the game can be one of his own species', as long as it can be played in his cell with simple equipment strictly according to rules which are written down before play and cannot change after play starts, and it has a finite endpoint. The game and execution are televised planet-wide, and watching the desperate prisoner try to spin the game out as long as possible is very popular entertainment; the record is sixteen days. The hero knows a rescue ship might take a year or more to arrive, so chooses to play Towers of Hanoi with 64 discs until rescue arrives. When the locals realize they've been had, they are angry, but under their own rules there is nothing they can do about it. They do change the rules, which will apply to any future prisoners. This story makes reference to the legend about the Buddhist monks playing the game until the end of the world, and refers to the game as arkymalarky. (The slang term "malarky", meaning nonsense, pre-dates this story by at least 30 years. )