How does this work? (7up online number 'guesser')

daymobrew

http://digicc.com/fido/

This is a Macromedia Flash 'movie' that guesses a number that you choose.

Procedure:
- Write down a random 3 or 4 digit number. Use different digits.
- Jumble up the digits to create a new number.
- Subtract smaller number from larger number.
- Circle one of the digits in your answer but not a zero.
- Enter the other 2 or 3 digits into the web page, in any order you choose.
- Circled number is displayed!

Presumably there is some formula for discovering the circled number. What is it?

breadmonkey

Hmm. I had a look but can't figure it out. Is there some handy theorem that deals with subtracting numbers which contain the same digits?????

Sev

This is just a quick guess, with little analysis..

But I think after you take the smaller number from the bigger number, you always get a number divisible by 9. Every number that is divisible by 9, has its digits add up to 9, or else, the sum of its digits will also be divisible by 9. So after you tell it the other 2 numbers that make up that sum, it can deduce the final (non-zero) number fairly easily.

Sev

Its easy to demonstrate why when you take away the jumbled number you get a number divisible by 9.

Represent the original number like so...

1000a + 100b + 10c + d

Then the jumbled number would be represented something like this...

10a + 1000b + c + 100d

and when you subtract, youll always get a number of a form similar to..

9990a -900b + 9c - 99d

And its then easy to see where the divisibility by 9 comes from.

breadmonkey

Ah, very good!

billstraighten

its like the magic thing on ebaums world all to do with the no.9