General Numeral, who liked to boast of his exploits, was riding through town. He encountered two young nobles, Sir Lancelot and Lady Elaine.

General Numeral boasted, "I've solved at least 10,000 math problems."
Sir Lancelot replied, "Surely you solved fewer than 10,000."
Lady Elaine said, "I suppose you solved at least one."

How many math problems has General Numeral actually solved, if only one of these three statements is true?

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