# How is this trick done? **URL:** \ **Category:** Factual Questions\ **Created:** [January 16, 2006, 1:32pm UTC](https://boards.straightdope.com/t/how-is-this-trick-done/340212 "2006-01-16T13:32:03Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![cards](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@cards](https://boards.straightdope.com/u/cards)\ **Post date:** [January 16, 2006, 1:32pm UTC](https://boards.straightdope.com/t/how-is-this-trick-done/340212/1 "2006-01-16T13:32:03Z")
I’ll bet this has been done on the board before, but I didn’t it find on a search. [http://digicc.com/fido/](http://digicc.com/fido/) So, how does it work? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [January 16, 2006, 1:38pm UTC](https://boards.straightdope.com/t/how-is-this-trick-done/340212/2 "2006-01-16T13:38:49Z")
The difference between a multi-digit number and any of its “anagrams” is always a multiple of nine. Proof on request. The sum of the digits of a multiple of nine is itself always nine (or a multiple thereof). Proof on request. So Fido adds up the numbers you type in, if the result is multiple digits then he adds 'em again, and once he’s down to a single digit he subtracts it from 9. He doesn’t let you circle 0 as he couldn’t tell if you’d circled a zero or a nine. ---
**Author:** ![don\_t\_ask](https://avatars.discourse-cdn.com/v4/letter/d/e68b1a/32.png) [@don\_t\_ask](https://boards.straightdope.com/u/don_t_ask)\ **Post date:** [January 16, 2006, 1:47pm UTC](https://boards.straightdope.com/t/how-is-this-trick-done/340212/3 "2006-01-16T13:47:52Z")
When you do the first few steps you end up with a number that, when you add the digits is divisible by 9. Say 2205 or 99 or 495. The number you type in provides the answer, it is the ndifference to the next multiple of 9 from the total of the digits. 6894 4689 = 2205 6894 4986 = 1908 9864 6894 = 2970 etc ---
**Author:** ![cards](https://avatars.discourse-cdn.com/v4/letter/c/ecd19e/32.png) [@cards](https://boards.straightdope.com/u/cards)\ **Post date:** [January 16, 2006, 2:49pm UTC](https://boards.straightdope.com/t/how-is-this-trick-done/340212/4 "2006-01-16T14:49:56Z")
> [@Malacandra](#): > > The difference between a multi-digit number and any of its “anagrams” is always a multiple of nine. Proof on request. > > The sum of the digits of a multiple of nine is itself always nine (or a multiple thereof). Proof on request. > > So Fido adds up the numbers you type in, if the result is multiple digits then he adds 'em again, and once he’s down to a single digit he subtracts it from 9. He doesn’t let you circle 0 as he couldn’t tell if you’d circled a zero or a nine. Thanks, I get your first two points, but I’m fuzzy on the last step, where you “adds 'em again”. Can you provide an example? ---
**Author:** ![Malacandra](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@Malacandra](https://boards.straightdope.com/u/Malacandra)\ **Post date:** [January 16, 2006, 2:59pm UTC](https://boards.straightdope.com/t/how-is-this-trick-done/340212/5 "2006-01-16T14:59:39Z")
Think up: 9631 Rearrange: 1963 Difference: 7668 You circle: 6 Fido adds: 7 + 6 + 8 = 21. It’s more than one digit, so Fido adds 2 + 1 = 3 Fido subtracts 3 from 9 to yield 6.