## Rank Math Trick

*December 3, 2010 at 7:04 am* *
1 comment *

The Amazon sales rank for *Math Jokes 4 Mathy Folks* fluctuates between 20,000 and 300,000. The highest rank to date was 11,394, which occurred July 7, 2010, the morning after a review of the book appeared in Maria Miller’s Homeschool Math Blog and in her email newsletter.

Today, the Amazon sales rank was 113,113. Cool number, eh? Reminds me of an arithmetrick:

- Take a three‑digit number
*abc*. Then, write it twice to make a six‑digit number*abc*,*abc*. (For instance, if you chose 113, then your six‑digit number would be 113,113.) - I’m feeling lucky, so divide by 7.
- Hmm… I’m not feeling quite as lucky now, so divide by 11.
- Uh-oh. I no longer feel lucky at all. Divide by 13.
- Check your result. Should be the three‑digit number you started with,
*abc*.

The following joke is a hint to why this trick works, in case you haven’t already figured it out:

Teacher: Can you find the prime factorization of 1,001?

Student: I didn’t even know it was lost!

Entry filed under: Uncategorized. Tags: arithmetrick, prime factorization, puzzle, rank, trick.

1.xander | December 3, 2010 at 8:51 amSo, clearly, there was going to be a trick at the end. I’ve seen these kinds of problems before, and I like to think that I am a smart cookie (though my wife calls me a smart Alec)! We started by dividing by 7, so, without bothering to read on, I went about proving that abc,abc is divisible by 7.

Having done that, I got to the next step. Division by 11 is easy! \o/

So, my number is divisible by 77. Cool. That’s kind of nifty. On to the last step. Division by 13, eh?

Wait a minute…

7x11x13 = 1,001.

Crap.

Now I feel dumb. 😦

Remember to read to the end of the problem before answering, xander! D’oh!