From The Collaborative International Dictionary of English v.0.48:

umpteen \ump"teen\, a.
   An indefinite number, usu. more than ten and less than one
   hundred; a lot. Often used hyperbolically, and usually
   expressing the notion of more than the usual number or more
   than I would like. [Colloq.] "I've told you umpteen times not
   to do that."
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