## EE. Tossem Beaver Mathemagician Art Benjamin explains some of the tricks of his trade!

1. ### strauss said,

August 8, 2008 at 6:02 am

A listener writes:

Can you explain how the FIDO PUZZLE works? it has sent me totally crazy! Please let me know how this works.

Hi, this uses the same principle as the trick that Art Benjamin described a few weeks ago:

In the Fido Trick, you take a number, scramble it to get another number and subtract.

The key is that this final number must be a multiple of 9.

Why is that? The remainder of any number, when you divide by nine, is the same as the remainder of the sum of its digits.

(I.e. both 97 and 9+7 have a remainder of 7 when you divide by 9) Since the original number and the scrambled number have the same digits, they must have the same remainder.

So the final number, their difference, must be a multiple of 9.

What good does that do? Just as Art does, the Fido Puzzle now can work out what digit you’ve left out by knowing that the digits in the final number have to sum to 9!

For example:

starting with 5921 (has remainder 8 when you divide by 9)
scramble to get 1295 (also has remainder 8)
subtract to get 4626 (which has to be a multiple of 9)

Now suppose you pick digits 4, 6, and 6
These sum to 16. But the total of the digits has to be a multiple of 9, since the mystery number is itself a multiple of 9.
Voila, the missing digit is 2

Thanks for writing!

Chaim

2. ### Ann Helmbeck said,

September 24, 2009 at 11:43 am

If I understand this…..you would go up to the next multiple of 9 which would be 18 and subtract the sum of the digits, 16, to get the anwer 2?