Monday Morning Fun

[TB Roye]

Here is a little fun for a Monday Morning. If you figure out how it is done please post the answer. http://digicc.com/fido/

Tom

[TJG]

After you calculate the difference, look at the answer. Add the digits of the answer together and they should be divisible by nine.

For example, if you chose 9871 and then subtract from it 1798, the difference is 8073. 8 + 0 + 7 + 3 = 18 (which is divisible by 9).

So, when you give it 3 of the 4 digits, it adds them up and figures out the next higher multiple of nine and subtracts the sum of the digits you gave it from that number. In the above example, if you provide 780, it adds them up and gets 15. Since 15 > 9, it goes to the next multiple of 9 (18) and subtracts 15 from 18 and gives you 3.

The rules prevent you from encountering the problems - you can't circle 0 and they want the number to be random. If the number had only one digit, such as 1111, then the difference would end up with 0.

[radhak]

nicely explained, TJG.

To make it even less mystifying, let's see how a 4 digit number looks like :

(say) abcd, where each letter is a numeric digit.

but abcd = 1000 x a + 100 x b + 10 x c + d (because a is in the 1000th place, etc).

so if we make it = dcab = 1000 x d + 100 x c + 10 x a + b

assume the 2nd number is bigger, so need to subtract abcd from dcab,

dcab - abcd =
1000 x d + 100 x c + 10 x a + b
- ( 1000 x a + 100 x b + 10 x c + d)

= 999 x d - 990 x a - 99 x b - 90 c
= 9 x ( some number)
= multiple of 9!!!

That point onwards, TJG's explanation works.

[Ed62]

Does anyone have a bottle of aspirin? My head hurts.

Ed

[jackellis]

It uses an old trick I learned in grade school for checking the sum of a list of numbers called "casting out nines".

TJG and Radhak, do you still have your slide rules?