1905, "of an indefinite number," originally Morse code slang for "dash," influenced by association with numerals such as twenty, thirty, etc.
But writing reminiscences of umpty Squadron's early days is a melancholy business.
Over there a formation of A flight, umpty Squadron, will perhaps be droning back from a hundred-mile reconnaissance.
And without the aid of a guide we located this umpty Umpt street.
Of any large unspecified number: exhausted all the encomia in your vocabulary on umpteen reviews
[fr WWI; said to have been first used by British military signalers during World War I to disguise the number designations of units]