### Carnac The Magnificent

Do you remember this recurring Johnny Carson role where he’d “divine” an answer and then open an envelope to reveal the question? You can do the same with numbers!

Ask your friends to pick a number from 1 to 31. Then double it, add 10, cut that result in half, subtract the number they started with, and—to their astonishment—reveal their result you’ve already written: 5!

It always works! Here’s the math: Let’s say ‘N’ is the number. Double it = 2N. Add 10 = 2N + 10. Cut that result in half = N + 5. Subtract the original N, and you’ve got 5!

I did this once with a class of sixth graders who were visiting me at the office. As we wrapped up, I said I had a “quiz” to give them and offered a prize if their answer (that they’d have to write on their paper) matched a number I had already written down. When we got to the end of the “quiz” and all of us revealed our number 5 at the same time (and they realized they had ALL won a prize), pandemonium broke out!

### Number 9

More than a chant from The Beatles’ “White Album,” the number 9 can help easily spot a transposition error—you know, writing \$1.24 instead of \$1.42. The difference is 18 cents—a multiple of 9. In fact, the difference between any two transposed numbers will always be a multiple of 9. (Contact me for the algebra behind this!)

This fact could come in handy, for example, when reconciling your checkbook and bank statement. You show a balance of \$22,300.54; the bank shows \$23,200.54. You’re off by \$900. As 900 is a multiple of 9, check your entries for a transposition error.