Roman Numeral Puzzle

February 3, 2012

The Super Bowl is the championship game of the American league of professional football teams — and an annual cultural event. The first Super Bowl, won by the Green Bay Packers under head coach Vince Lombardi, was in 1967, and wasn’t even called “Super Bowl” at the time; the name didn’t attach to the game until Super Bowl III, when Joe Namath of the New York Jets guaranteed a victory. Roman numerals have been used to designate the Super Bowl ever since. The game this year, between the Boston Patriots and New York Giants, is Super Bowl XLVI; you can solve today’s exercise while you watch the game on Sunday evening.

John D. Cook turned the wacky roman numerals of the Super Bowl into an exercise at his blog; he was inspired by an advertisement for Super Bowl XLVI on a pizza box. Cook asked his readers to compute how many numbers can be expressed as roman numerals without duplicating any of the symbols I, V, X, L, C, D or M.

Your task is to compute the number of roman numerals that have no duplicate characters. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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