Hannah Williams, 23, succeeded in solving the Isis Adventure puzzle, which involves trying to open a metal ball, then solving the clues hidden inside to find one of 19 gold coins hidden around the UK.
Ms Williams, a teacher at Oakham School, which charges annual fees of up to pound;23,850, spent endless hours puzzling over how to open the aluminium ball, which is constructed in layers and covered in Egyptian symbols.
"I really couldn't believe it when finally the puzzle ball began to unscrew," she said. "My hands were shaking, I was so surprised."
Inside the ball she found a booklet containing 10 encrypted clues, each of which she needed to work out to win the prize. The clues led Ms Williams from Rutland to North Yorkshire, where she found the winning pyramid hidden in a jeweller's shop.
"Inside the shop I found an Isis pyramid, which contained my winning pound;500 coin," she said. "The one I found had been in the shop since June of last year, and no one had managed to decipher it."
The puzzle, which was featured on BBC television's Dragons' Den show for entrepreneurial inventions last year, was the brainchild of inventor Andrew Reeves, who invested more than pound;200,000 over three years in its development.