What is the shortest period of time that an independent country has existed?
The probable answer is a day and the country was Carpatho-Ukraine.
Following the start of the Nazi dismemberment of Czechoslavakia, on 15th March 1939 the Carpatho-Ruthenia region of Czechoslovakia declared independence. Its head of state was the Reverend Avgustyn Voloshyn and its capital was Khust. A day later Hungarian troops marched in and seized the territory, which is now part of Western Ukraine.