## Cocktail Party Math

If there is anyone reading this blog thinking about teaching math, there are papers to grade, emails to answers, and meetings to go to. It isn’t all as glamorous as it looks. But you occasionally get a day when a colleague, perhaps Paul Argazzi, drops in and gives you a great new math trick. That’s when you know you’ve made the right choice. Here’s the trick. My choices are indicated in parentheses.

Paul walks in and says, give me a book. I hand him one from the shelf. He leaves through a couple of pages, gives it back to me, and says, pick a three digit number. (439) I do. He says to make sure the 100’s and 1’s digit are two or more apart. I got lucky and don’t have to re-pick. Okay, he says, take that number and flip it around so that the 100’s becomes the 1’s and vice versa. (934) Now subtract the smaller (439) from the bigger number (934), and call the result A (495). Then, he said, take A (495), spin it again, call that number B (594), now add A to B (1089). Then he told me to ignore the ones place and take the digits in front of the ones place (108). He said find that page in the book. I did. Then he told me to take the number in the ones place (9) and find that number word in the first line of the page. (So I looked for the ninth word in the first line of the page. It read “meaning”.) Then he asked me, is the word “meaning”?

Pretty cool, huh? So here’s the question. How does it work?