Five and Fifteen-Seventeenths Percent

Five and Fifteen-Seventeenth Percent

Film buffs may recognize the title of this article as coming from The Maltese Falcon,

an early example of film noir and the directorial debut of the great film director, John Huston, son of Walter Huston, who had a brief walk-on in the movie and, seven years later, won an Academy Award in another of his son’s films: The Treasure of the Sierra Madre.

In the denoument of the movie, Casper Gutman, the character played by Sydney Greenstreet, calculates that the “additional expenditure in time” of spending another year looking for the “black bird” after having spent “17 years on the quest” amounts to five and fifteen-seventeenth percent. It takes him about a second to calculate, in his head, the percentage of one-seventeenth. This scene in the movie always fascinated me but not until recently did I wonder how he might have done it. What simple arithmetic trick would allow one to quickly calculate the percentage for 1/17.

I don’t know why it took me 40 years to look for a shortcut but when I did, it came fairly quickly. You just divide 17 into 100. It goes five times (17 times 10 is 170, half of that is 85, which is 17 times 5. 85 from 100 is 15, hence 15 seventeenths. Five and fifteen –seventeenths.

Had it been 18 years instead of 17 then 18 times five is 90. 90 from 100 is 10. So the answer would be 5 and ten-eighteenths or 5 and five-ninths. Likewise 16 years would mean 6 and a quarter percent.

So why seventeen, and not 16 or 18? Well listen how much better “five and fifteen-senventeenth percent rolls off of the tongue, then does six and a quarter percent or five and five-ninths percent.