Want to let me read your mind?

Just cleaning up the ol' bookmark folder and came across http://www.digicc.com/fido">this cool little trick.

liitttlllee creepy.....


but fun


lost

I'm smarter than a javascript.

It's a fundamental mathematical principle.

I used a calculator even. Picked a number and a jumble specifically to yield a result of 1999. (1)999. It told me my circled digit was a 9, ergo it was wrong.

It looks like I broke the mathematical principle then. I admit it took me 20+ tries.

I started with my favorite numbers and after I ran out, I started using numbers chosen to garner a specific resultant sum, trying to figure out how it worked. Like I said, I was over 20 tries in...I was just picking numbers at that point. I kinda stumbled in it, now randomly choosing numbers to try to find the right combo, I'm having a hard time even finding a number that makes a total of 1999. It's like I know there is no four-digit number which can be jumbled to yield a total of 2000. I'm starting to think Pokerfan was right and chalk it up to calculation error.

What makes it interesting is this...if you simply choose a 4-digit number without doing the math and insert 3 digits...it still gets the fourth digit every time I tried it. (only 3 times) Now...that's creepy.

Just curious, what was the initial number?

Any number that results from the action must be a number that is a multiple of 9.

trying to replicate the result. I'm honest enough to admit I likely screwed-up the math. Calculators are only as good as the idiots hitting the buttons. :dunce:

I am laughing, with my mouth open!

How does it do that?

:wow:

The same principle is also used in an old accounting trick as a sorta checksum.

111-111=0

Enter 0.

It spits out 9.

It's indistinguishable from 9.

Here's the analysis from Dr. Math"
_____________________

Date: 05/12/2004
From: Doctor Roy
Subject: Re: Solving the Fido Puzzle

Hi Karen,

Thanks for writing to Dr. Math.

The trick has to do with divisibility by 9. Try the first part of the experiment again. Take any number (it doesn't really have to be 3 or 4 digits long, I imagine that's just so the computer has it a bit easy). Mix up the digits and perform the subtraction.

Now, divide the result by 9. You should come out with a whole number. In other words, the resulting difference should be divisible by 9. This works no matter what original number you pick. If you are familiar with number theory, the proof is simple enough. If not, just take my word for it that the difference will always be divisible by 9.

So, we have a number divisible by 9. One property of numbers divisible by 9 is that the sum of the digits of such numbers is also divisible by 9.

For example: 4059 is divisible by 9. 4+0+5+9 = 18. 18 is divisible by 9, so 4059 is divisible by 9.

4057 is NOT divisible by 9. 4+0+5+7 =16. 16 is NOT divisible by 9, so 4057 is NOT divisible by 9.

Let's use 4059 for now. If you pick 5, you enter 409 into the program. The program adds the digits up: 4+0+9 = 13. It finds the smallest number that can be added to 13 to get a multiple of 9. In this case 5:

18 - 13 = 5

So, 5 is the missing number.

That's why you are not allowed to pick 0. If the criterion is simply divisibility by 9, then the program is unable to tell the difference between 0 and 9.

For example:

4059 --> 459 ---> 4+5+9 = 18

The smallest number that can be added to 18 to get a multiple of 9 is 0. The other number that can be added to get a multiple of 9 is 9 itself. So, both 0 and 9 are possible choices. But since you are not allowed to choose 0, the program will give you 9.

Try it out. Enter 459 into the machine. It will not give you 0, which is the number we chose above. It will give you 9 instead.

Does this help? Please feel free to write back with any questions you may have.

- Doctor Roy, The Math Forum
_____________________

Wikipedia has a more general http://en.wikipedia.org/wiki/Casting_out_nines">article on the general principle and its applications.