It works on an ancient numerological phenomenon known as “casting out nines”. Here’s what happens:



1) Pick any 4-digit number (actually, any size number will work, regardless of how many digits it contains): 2958

2) Scramble the number: 9285

3) Subtract the small from the larger: 6327

Aha! Step 3 is where the real magic takes place! Whenever you take any number

(regardless of how long), scramble it, and subtract one from the other, the answer will

always be divisible by 9! 6327 / 9 = 703 - Son of a gun – it works!

4) Now, circle one digit in the number: 6327 (Alright, I couldn’t circle it – it’s the 2!)

5) Scramble the remaining digits: 763



Now, how does the web site figure out which digit you circled? Easy! This is where the actual “casting out nines” comes into play. If you take any number divisible by nine (like our 6327 above), adding all the digits together will yield a number that is, again, divisible by 9:

6 + 3 + 2 + 7 = 18 - Yep, 18 is divisible by 9! But check it out – do the same thing with the digits in the number 18 – add them together and you get (trumpet fanfare): 9! Basically, if you take any number at all that’s divisible by 9, and keep adding the digits together, you’ll eventually end up with the digit 9. Now, add up the digits in 763: 7 + 6 + 3 = 16, and 1 + 6 = 7. Now, subtract the 7 you just got from 9 and you get – drum roll please – the 2 that you had magically circled! That’s because when you cast out nines for a number divisible by nine, you end up with…9. When you take the original number that was divisible by 9 and remove one of the digits, the “cast out nines” value of the resulting number will be 9 minus the number you circled. Conversely, if you take 9, and subtract from it the “cast out nines” value of the resulting number after you remove a digit, the answer will be the number you circled!



They didn’t really have to tell you not to circle a zero. Let’s say you picked the number 8207:



8207 Original number

- 7802 Number scrambled

------

405 Difference



405 Circle the 0



4 + 0 + 5 = 9

Remove the 0, add the remaining digits: 4+5=9

9 – 9 = 0, so it would still work (if the web site is doing it the easy way!)



Groovy, huh? Tomorrow’s lesson will be on the Moebius strip, a 3 dimensional object with only 1 side and 1 edge!