"The Most Incredible Thing" is number 190 in the Hans Christian Andersen Center's register of Andersen's literary works, i.e. no. 190 in the category fairy tale (the range 1 - 300).
"The Most Incredible Thing" was first published in English September 1870, cf. the bibliographic description (in Danish) in : H.C. Andersen-Centrets bibliografiske optegnelser:
The Most Extraordinary Thing
The first Danish edition (October 1870): Det Utroligste. (Et Eventyr).
The work was published later (30 March 1872) as a part of Nye Eventyr og Historier. Tredie Række. Ny [første] Samling. 1872 [Danish title]. (Number 335. BFN 1017. Category/genre: Fairy tale collection).