Stumped: Stuck - unable to proceed, often regarding being confounded by some intellectual puzzle.
Some authorities have supposed that this derives from the development of the road system in the USA. When these highways were being built the stumps of sawn down trees could be no more than 15 inches tall. This was fine for the high axle wagons until rain softened the soil, at which time wagons would sink into the mud and were 'stumped'. This is a good story, albeit one that doesn't come packaged with any real evidence. Others have suggested that it might be from cricket, in which a batsman is out if the wicketkeeper removes the stumps with the ball when the batsman is out of his ground. This explanation is also lacking supporting evidence and in any case doesn't really match the meaning of the expression.
It is more likely that the term derives from ploughs sticking when they hit tree-stumps. The USA origin is certainly correct though. All of the early citations of the phrase originate from there; for example, Seba Smith's Letters of Major Jack Downing, 1833:
"My Good Old Friend, - I'm stumped. I jest got a letter from the Gineral."
The term is pre-dated by the term 'stumper', which was US slang for a difficult poser. This was cited in an 1807 edition of the New York magazine Salmagundi:
"They happened to run their heads full butt against a new reading. Now this was a stumper."