Stumped

"I'm stumped," said a friend in the States, and that got me thinking.  A stump is the remains of something cut off--a tree stump remains when you cut the tree, a stump remains when you amputate an arm or leg.  But where does the term "I'm stumped" come from?

It means to be confused, not to know the answer.  But where does it come from?  Another mystery!  So we're all stumped!