What is the origin of the strange idiom "einen Türken bauen"?
I have already checked wiktionary, and they present a few alternatives. All these alternatices are insufficient IMO, as they all smell like someone invented them to make the idiom sound plausible.
These stories all are hard to refute, but I don't believe them.
When the "Kaiser-Wilhelm-Kanal" was inaugurated, the hymn of every State that had sent a representative was played. Because the hymn of the Turks was not available and instead the musicians played "Guter Mond, du gehst so stille durch die Abendwolken hin."
In the age of Rokoko Johann Wolfgang Ritter [..] built a so called "Mechanischer Türke" who won chess against some of the most renowned masters. Later it was revealed, that in fact the puppet did not think, but a human inside played.
Swiss Military speech: Türgg - maneuver
In the 15th to 17th century, there was great fear of a turkish invasion. This seems to have been used to create high taxes from nothing (to be used for a counter-invasion), which were used for something completely different then.