Clever Stuff!

[Annie]

To help keep your mind agile and fit, can anyone work out how this works?

1) Go to the link below. After reading each window, click on the boy in the lower right corner of the picture.

2) In the last window type in your answer in the white box using the Keyboard (there is NO cursor).

3) Watch the paper in the boy's hand. You will be amazed. And no, I don't know how it's done.click here:

http://digicc.com/fido/

[JKC]

When you take the two numbers away you always get a multiple of 9 (like when you make transposition errors in accountancy). As we all know the digit totals in multiples of nine always add to nine so they just pick a number to make the total of the digits a multiple of nine. Simple really.

[Annie]

Well as you've let the cat out of the bag you may as well get the low down..............

The Think Clear Puzzle

This little puzzle stems from properties of our old friend the digit 9. The
difference between any number and the jumbling of its digits produces a multiple of 9.
Since most of us use the decimal system to communicate numbers, we can express any number as a sum of the digits times powers of 10. Symbolically, the number N can be expressed as N = 10^n*A1 + 10^(n-1)*A2 + ...+An where A1,A2,...An are the n digits of the number. For example if we choose the number 3141 in powers of 10 it becomes 10^3*3 + 10^2*1 + 10*4 + 1 or 1000*3 + 100*2 + 10*4 +1 = 3000+100 + 40 +1 = 3141.
Let us subtract symbolically a 4 digit number and its jumble. Let N = 1000A1 + 100A2 + 10A3 + A4 Now we know there are 24 possible ways to jumble A1 to A4. Eg., A4A3A2A1, A3A4A2A1 etc. Let J = 1000A2 + 100A1 + 10A4 + A3. Now if we take N-J we are free to subtract any term in J from any term from N (Commutative law of addition) for all terms and add them up. In our example, N-J = 1000A1-100A1 +100A2-1000A2 +10A3-A3 + A4-10A4. This factors to N-J = 900A1 – 900A2 + 9A3 - 9A4 = a multiple of 9. Notice that no matter how we arrange the A's in the jumble there is always a corresponding A in N such that when we subtract two terms, we will have a multiple of 9 for each term of the difference-pair. Therefore, the difference between any number and its jumble (with or without regard to sign) is a multiple of 9.
The following Theorem will enable us to complete the puzzle.
Digital Root Theorem:
The digital root of an integer x is 9 if 9 divides x or the remainder of x/9 if 9 does not divide x.
The digital root of a number is the repeated summing of the digits until you get a single digit. For example, the Digital root of 1234567 = 1+2+3+4+5+6+7 = 28. 2+8=10.1+0 = 1.
Using the theorem, 1234567/9 = 137174*9 + 1. So the remainder is 1 as we would expect. Now if we have a number that is a multiple of 9 say, 12345678 then we get a remainder 0 which implies 9 is a divisor as is the case in difference the puzzle. Then taking away a digit d will leave a new sum of 9 - d. So if we circle the 8 in 12345678 we will have a new digital root of 1. So 9 – d is 1 and d is 8.
The Puzzle cleverly says to pick non-zero so to hide the 9 property. You will always get 9 if you pick 0 because 0 lets the digital root stay at 9 and 9 - 9 = 0.
I will summarize:
Using Excel, you can dazzle your friends at work without the boss catching you on the web of course.
Rows 3 and 6 are the formulas 1,2,4 are input. 6 is also the answer.
A B
1 Number =>
2 Jumble =>
3 Difference =ABS(A1-B1) Take the positive number
4 Picked digit=>
5
6 Digit picked =9 - MOD(B4,9) Justified by the digital root Theorem
Cino <st1:date Year="2003" Day="27" Month="11">11/27/2003</st1:date>

OK? :thumbsup:

[JKC]

Looks like a load of waffle that says the same as I said. Sorry about spoiling the puzzle, I suppose it is the Maths Teacher in me.

[Annie]

Looks like a load of waffle that says the same as I said. Sorry about spoiling the puzzle, I suppose it is the Maths Teacher in me.

Not at all! I'm just ashamed that I didn't spot it myself with my Accounts background. :bag:It's one of the first rules I was taught.

It's still worth having ago.

[Annie]

And another one..........

HERE (http://www.quizyourprofile.com/guessyournumber.swf)

I actually worked this one out all on my own loooooool :woho:

[MK Chris]

Is this place full of accountants?

That means you all have sloping shoulders!

[Annie]

I'm not quite an Accountant and here's the proof..... http://i32.photobucket.com/albums/d29/hungarianwonderwoman/Emotions/boy.gif

[JKC]

Only did it for 3 years and then trained as a teacher. Found myself doing 126+1 on the calculator one day and decided enough was enough.