Unique Words

Using Scrabble^® tiles, my sons were making anagrams. One would select four tiles, and the other would have to rearrange them to form a word.

This struck me as interesting, so I posed the following question to them:

Take four consecutive letters from the alphabet, and rearrange them to form a common English word.

How many solutions do you think there are? Before you solve the problem, take a guess. Can five words be formed from four consecutive letters? Maybe ten words? Or fifteen?

Okay, now solve the problem. Take your time. We’ll wait for you.

There are 23 ways to select four consecutive letters, and each set of four letters can be arranged in 4! = 24 ways. With 23 × 24 = 552 possibilities, it seems like there ought to be several solutions.

Were you as surprised as I was to find that there was only one?

But maybe I shouldn’t be too surprised. Lots of things in life are unique…

Always remember that you’re unique, just like everybody else.

Student: Do you believe in God?
Professor: Yes — up to isomorphism!

Then again, lots of things aren’t unique…

Don’t think you’re special. Even if you’re 1 in a million, there are still 7,000 people in the world just like you.

Here are two unique, non-math jokes…

How do you catch a unique rabbit?
Unique up on it.

How do you catch a tame rabbit?
The tame way!

2011 is Prime Time

It’s been eight years coming, but finally, a year that’s a prime number. This hasn’t happened since 2003, but 2011 is prime.

Express 2011 as a sum of consecutive prime numbers.

That can be done in several different ways.

As it turns out, 2011 is extra cool because it can be written as a sum of a prime number of consecutive prime numbers.

When will that happen again?

And finally…

What is the next year that will be a prime number and also be a sum of a prime number of consecutive prime numbers? (Wow, that’s a mouthful, ain’t it?)