"Prince Sigismund of Prussia first ascertained Anna's identity by relying upon her essentially correct answers to the series of questions he posed to her in 1932 through the offices of his brother-in-law, Prince Frederick of Saxe-Altenburg. At this time Sigismund was living in Central America, so he asked Frederick to carry out this mission. Frederick would not reveal Sigismund's questions or Anna's replies for many years, to avoid being accused of having supplied Anna with the answers. He later said she correctly identified her last meeting with Sigismund as being at the hunting lodge at Spala, in what was in 1912 the Polish provinces of Russia. Anna also recalled that Sigismund had stayed in the quarters of Count Fredericks, the minister of the court, and answered the 16 other questions quite accurately. While this was enough proof for Sigismund and by extension for Frederick, who had never met Anastasia as a child, it is very curious that anyone could recall such details 20 years after the event."
The Quest for Anastasia, p. 153. Klier and Mingay, 1999 edition.
I think that the last quoted sentence should be taken as the opinion of the authors, obviously, but the rest of this gives a sense of at least the kind of questions Sigismund posed to Andersen. Klier and Mingay also make reference to the "Anastasians", i.e. Andersen's supporters --- people like Lilburn and Aucleres --- feeling that Sigismund undermined his credibility by his support for Marga Boodts, the Lake Como claimant to be Grand Duchess Olga.