## Posts tagged ‘Art Benjamin’

### A Great Day for a Math Trick

Today is 7/11/13, and boy, have I got a great math trick for today! You’ll likely need a calculator.

- Multiply your age by 12.
- Now add the age of your spouse/brother/sister/friend/uncle/aunt/whomever.
- This should yield a three-digit number. Now, divide by 7.
- Then, divide by 11.
- Then, divide by 13.
- The result should be a number of the form 0.
*abcdef*…, with a 0 and a decimal point in front of a long string of digits. Add the**first six digits**after the decimal point.

Here’s the cool part. I don’t know your age, nor do I know the age of your spouse, brother, sister, friend, uncle, or aunt. But I do know that after you completed those steps, the result was 27.

Pretty cool, eh?

There are myriad math tricks of this ilk, but this one is my favorite. It’s based on a trick I learned from Art Benjamin, though I think the one above has more panache than his original. Decide for yourself.

- Choose a number from 1 to 70, and then divide it by 7.
- 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.

Just as with the trick above, the result will always be 27.

Regardless of which trick you prefer, have a happy 7/11! And if you’ve got a few hours to kill, you can try to solve the 7‑11 problem.

### Rectangles for Mathemagicians

Depending who you ask, *mathemagician* has at least two different definitions:

- A person who enjoys both math and magic. (Wikipedia)
- A person who is so good at math that the answers to math problems seem to come to them magically. (Urban Dictionary)

When professor Art Benjamin told Stephen Colbert that he was a mathemagician, Colbert asked, “What does that mean? Were those two words by itself not nerdy enough?”

Below is a math puzzle involving magic. To be precise, magic rectangles. But first, a little warm-up…

What do you call a quadrilateral with four right angles that’s been in a car accident?

A wrecked angle.

For the last several years, I’ve had the pleasure of creating puzzles for the Daily Puzzle Challenge at the NCTM Annual Meeting. A new set of four or five puzzles appears in each day’s challenge. The following puzzle, which appeared on Friday’s Daily Puzzle Challenge, involves rectangles and is my favorite puzzle from this year’s meeting.

A magic rectangle is an *m* × *n* array of the positive integers from 1 to *m* × *n* such that the numbers in each row have a constant sum and the numbers in each column have a constant sum (although the row sum need not equal the column sum). Shown below is a 3 × 5 magic rectangle with the integers 1-15.

Below are three arrays that can be filled with the integers 1-24, but only two of them can be filled in such a way as to form a magic rectangle. Construct two magic rectangles below; for the array that cannot be used to construct a magic rectangle, can you explain why not? More generally, can you determine what types of rectangles can be used to construct magic rectangles and which cannot?

### Five Online Math Favorites

According to Google, there are more than 121 million results for “math.” The following is an unordered and incomplete list of some of my favorite math things on the web.

**1. **I laugh out loud at the comics on xkcd.com, but I think my favorite joke on the site is the disclaimer that appears at the bottom of every page.

Warning: this comic occasionally contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).

But if you insist that I choose just one of Randall Munroe’s cartoons, I’ll pick Fields Arranged by Purity.

**2.** I used to watch really old, really bad movies with my father on Sunday afternoons (but only when the Steelers weren’t playing, of course). The following is a clip that I remember, now ubiquitous on YouTube.

**3.** The only thing better than a great a cappella song is a funny a capella song. The only thing better than that is a funny a capella song that involves numerous math puns. Thanks, Klein Four!

Finite Simple Group of Order Two – Klein Four

**4.** When my friend Art Benjamin was interviewed on *The Colbert Report*, Stephen Colbert said to him, “You call yourself a mathemagician. Now, what does that mean? Were those two words not nerdy enough by themselves?” Nerdy or not, Art is frickin’ amazing.

Art Benjamin Does Mental Math – TED Conference

**5.** The following is a quote I’ve seen numerous times on the web, yet I’ve never seen an attribution. I’ll post it here, and credit Anon, though I’m pretty sure it’s a rip-off from a similar quote by Eleanor Roosevelt — “Great minds discuss ideas; average minds discuss events; small minds discuss people.”

Small minds discuss persons. Average minds discuss events. Great minds discuss ideas. Really great minds discuss mathematics.