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Blaise Pascal: Problems
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Unfortunately, Pascal's invention served primarily as an early lesson in the vagaries of business, and the problems of new technology. Pascal himself was the only one who could repair the device, and the cost of the machine cost exceeded the cost of the people it replaced. The people themselves objected to the very idea of the machine, fearing loss of their skilled jobs.
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Pascal proceeds next to consider the similar problems when the game is won by whoever first obtains m + n points, and one player has m while the other has n points. The answer is obtained using the arithmetical triangle. The general solution (in which the skill of the players is unequal) is given in many modern text-books on algebra, and agrees with Pascal's result, though of course the notation of the latter is different and less convenient.
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Pascal went about the house tapping the china with his fork then dissappeard into his room only to emerge hours later having completed a short essay on sound. He used the same approach to all of the problems he encountered; working at them until he was satisfied with his understanding of the problem at hand. A few of his disocoveries stood out more then others, of them his calculating machine, and his contributions to combinatorial analysis have made a signifigant contribution to mathematics.
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