You arrive on the island with knights and knaves. Like usual, knights can only tell the truth and knaves can only tell lies. You wish to determine the truth of a rumor that one of the inhabitants has recently proved Goldbach’s Conjecture. What single question—answerable by “Yes” or “No”—can you ask of an arbitrary inhabitant in order to determine the truth?
I am stuck because there is only one inhabitant to ask and thus you have no basis for comparison of whether the one you are asking is a knight or a knave.
Truth table: $$\begin{array}{ccc} \mathrm{Answer}\backslash \mathrm{Fact} & y & n \\ \mathrm{Knave} & y & n \\ \mathrm{Knight} & y & n \end{array}$$
Since the table for the straight-forward question is $$\begin{array}{ccc} \mathrm{Answer}\backslash \mathrm{Fact} & y & n \\ \mathrm{Knave} & n & y \\ \mathrm{Knight} & y & n \end{array}$$ and the Knave lies when answering, "double inversion" occurs, giving you the true answer to the straight-forward question from both kinds of people.