Category Archives: Math

Math tricks

Today’s New York Times has the obit of arithmetic wizard Shakuntala Devi:

 In 1977, at Southern Methodist University in Dallas, she extracted the 23rd root of a 201-digit number in 50 seconds, beating a Univac computer, which took 62 seconds.

In 1980, she correctly multiplied two 13-digit numbers in only 28 seconds at the Imperial College in London. The feat, which earned her a place in the 1982 edition of the Guinness Book of World Records, was even more remarkable because it included the time to recite the 26-digit solution.

(The numbers, selected at random by a computer, were 7,686,369,774,870 and 2,465,099,745,779. The answer was 18,947,668,177,995,426,462,773,730.)

For the record, it took me 20 seconds to read the answer aloud, counting the time I needed to determine the number is in the septillions.

Her mental legerdemain was sharpened by the fact that her father was a lion tamer, a fact thatI hope gives you incentive to read the entire Times obit.

To show off for Times journalists in 1977, she answered the following:

questions

Answers below the fold.

Meanwhile, she wrote some books. For one of them, Amazon’s sneak peak shows, among other things, how to determine if a number is divisible by 7. I’ve been looking for that for years. Her method is a bit of brute force, but it works.

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Math problems

This is from a study guide my fourth-grade daughter received:

 

The calculation error gives the teacher the right answer, instead of 1/24.

Normally, I give stuff like this a pass, since anyone can make a mistake. But this particular teacher is a math specialist, and it’s the second time a study guide has had both an error in arithmetic and algorithm design.

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Pi games

Yesterday (3/14) was pi day, but I only saw this link today, to a game that estimates pi by dropping sticks on a cyber-mat.

Try it! And be sure to scroll up to read the explanation why it works.

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Is your birthday special?

Only quants can have fun with dates that doesn’t involve snogging.

Financial expert/blogger David Markel defines a special birthday as one where you can create a simple math equation from the date.

For example, David was born Dec. 5, 1960. That, of course, is 12/5/60, and 12 x 5 = 60. There are also special days for:

  • Addition (1/1/02 is an example)
  • Subtraction – (12/5/07)
  • Division – (8/1/08)

Fun idea, right? Not sure how you count European dating, where the date precedes the month, i.e., 12/5/07 would be 5/12/07.

Brushing that aside, here’s the big question: Over a 400-year arc (has to be 400 to properly handle the leap-year cycle), how many birthdays are special?

The answer, and the methodology, are here.

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