Can you figure out how they do this? Puzzle

[CJ Swartz]

http://digicc.com/fido/

After reading each window click on the boy in the lower right corner.
In the last window type in your numbers in the white box using your keyboard.
Then click on the boy in the lower right corner again

If it works for you like it worked for me, you will be amazed....and you may wonder, like me, how it's done. Usually I can see the gimmick in these things, but I don't see this one -- maybe you can...?

[MaryLynn]

I'm not a mathemetician; I'm a musician working as a bookkeeper. (Musicians make good bookkeepers because they can count to four--lots of times!)

But, a teacher once showed our math class about the wonderful power of nine. Take any number that is evenly divided by nine and add the digits of the number together--it will result in nine. As a bookkeeper, if something doesn't balance, I look for the difference and divide it by nine. If the difference is divided evenly, I look for a transposition of numbers. It isn't always the problem but it is a good test.

This test has us transposing numbers and then working with the difference of the two numbers. If you add together the numbers you typed in, for example: 515, added together you get 5+1+5=11, 1+1=2; subtract 2 from 9 and you get my missing number 7.

[Legacy~Art]

Now that is clever cos i picked an number then before i wrote it down i changed my mind lol and it got it write too...

[CJ Swartz]

Originally Posted by MaryLynn

I'm not a mathemetician; I'm a musician working as a bookkeeper. (Musicians make good bookkeepers because they can count to four--lots of times!)

I see your point!

Originally Posted by MaryLynn

But, a teacher once showed our math class about the wonderful power of nine. ...This test has us transposing numbers and then working with the difference of the two numbers. If you add together the numbers you typed in, for example: 515, added together you get 5+1+5=11, 1+1=2; subtract 2 from 9 and you get my missing number 7.

O.K., but then how did it get my answer when it was 8, when it was 1, when it was 4... ? There does have to be a gimmick, but how does the gimmick work with so many different numbers, AND it doesn't tell you HOW to transpose the numbers -- we are free to do it anyway we want...?

[MaryLynn]

What works is the fact that the difference between one number and a transposition of that number will be evenly divisible by 9, regardless of how you transpose the numbers.

4321 minus 1234 equals 3087: 3+0+8+7=18, 1+8=9
4321 minus 3412 equals 909: You get the idea.

In the game, regardless of which numbers you supply, the computer adds those numbers and subtracts the result from 9, resulting in the missing number. (It doesn't want to have 0 as a missing number)

5389 minus 3958 equals 1431: 1+4+3+1=9

If I give the computer 413, or any combination of those digits, the computer adds them together and subtracts from 9. Result: missing number is 1.

[Legacy~Art]

MaryLynn WOW i am so impressed!!!

[MaryLynn]

Thanks, but please don't ask me to figure out 2x+y=z My brain shuts down!

[CJ Swartz]

Excellent, MaryLynn! I've heard that rule before, but never saw how it could be used in something like this -- thanks for clearing up the "mystery".