## Archive for December 28, 2010

### Permutations

Tonight at dinner, my wife told Alex that he had to eat his carrots. “How many?” he asked. There were three on his plate. “Two,” she responded. (For what it’s worth, I deplore these dinnertime negotiations. I put three carrots on his plate — I expect him to eat three carrots. If I only wanted him to eat two, I would have given him only two. On the other hand, my kids are 3½ and they actually ask for broccoli, edamame, carrots, kale, and a host of other veggies, so I can’t really complain.)

Alex then turned to his brother and asked, “Which two should I eat, Eli?” He picked up Carrot A and Carrot B and asked, “These two?”; he then returned Carrot B to his plate and picked up Carrot C and asked, “These two?”; and, finally he picked up Carrot B and Carrot C and asked, “Or these two?”

I was pretty psyched about Alex’s “proof without words” that _{3}*C*_{2} = 3.

Of course, we all know how cool permutations are, since all of our inboxes have been filled by the text of a letter written by Graham Rawlinson to *New Scientist* in 1999. You know the one, which purported “that randomizing letters in the middle of words had little or no effect on the ability of skilled readers to understand the text.”

For iancstne, you utadnnersd this snenctee celalry eevn tughoh the ltetres of msot wodrs are out of oedrr.

It is inaccurate to say that there is “no effect,” however. A follow-up study showed that college students experienced a 12% decrease in overall reading speed when confronted with sentences containing transposed letters. Quite a few of the other statements in the email that we received — for instance, that there was a study done at Cambridge (there wasn’t) — were also inaccurate. Even the email itself is misleading, ostensibly written to enhance the desired effect and further prove its point; in truth, almost half of the words contain only two or three letters and are spelled correctly.

But don’t blame Graham Rawlinson for all of that. That’s just the way things work in cyberspace.

Okay, enough already. How ’bout some math?

How many permutations exist for the word PERMUTATIONS?

And last but not least, some permutation jokes…

Combinatorists do it in every possible permutation, but they do it discretely.

What do you get if you add Daytona Beach, Pismo Beach, Palm Beach, and South Beach in various permutations?

Sums of beaches.