Ta Da! Art Benjamin Shows His Magic in Times Pop Quiz

February 1, 2010 

"Mathemagician" Art Benjamin showcased some of his methods in a "math quiz" published in The New York Times Education Life Section.

Benjamin (Harvey Mudd) revealed ten mathematical concepts from his DVD course “The Joy of Mathematics” and his book Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks.

Here's one example.

"Choose a number from 1 to 70 and then divide it by 7 (Use a calculator, but you’ll need one that has at least seven decimal places). If your total is a whole number (that is, no digits after the decimal point), divide the answer by 7 again. Is there a 1 somewhere after the decimal point? I predict that the number after the 1 is 4. Am I right? Now add up the first six digits after the decimal point."

The answer is 27!

Benjamin explained, "The six fractions 1/7 to 6/7 have the same repeating sequence of six numbers after the decimal point, each fraction starting with a different number in the sequence 142857. Think of these numbers as in a circle...and going around that circle forever."

"The first number after the decimal point in the decimal version of 1/7 is 1 (.142857); of 2/7, 2 (.285714); of 3/7, 4 (.428571); of 4/7, 5 (.571428); of 5/7, 7 (.714285); and of 6/7, 8 (.857142). Adding 1, 4, 2, 8, 5 and 7, you always get 27."

Benjamin recently showed off his mental math skills on Comedy Central's The Colbert Report. Host Stephen Colbert didn't pull any punches. In between asking ridiculous questions such as which numbers are conservative and which are liberal, he surprised Benjamin with several math problems and even had a calculator at the ready to verify Benjamin's answers. Naturally, Benjamin got them all right.

Watch the clip of Art Benjamin's interview on The Colbert Report here.

Source: The New York Times (December 30, 2010)