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# Re: OT: Unbelievable

From: Mark J. Reed Friday, June 6, 2003, 19:31
```On Fri, Jun 06, 2003 at 08:24:55PM +0200, BP Jonsson wrote:
> My fiancee was directed to this:
>
> <http://mr-31238.mr.valuehost.co.uk/assets/Flash/psychic.swf>
>
> Is there a mathematical explanation to this?
> Not that I would understand such an explanation,
> but I'd like to know if there is one.
That's a strange question.  Of COURSE there's a mathematical explanation.
I mean, what's the alternative?  A psychic computer program?  :)

The result is always a multiple of 9, and all multiples of 9 have
the same symbol associated with them (but every time you go back to the
page they change which symbol that is to make this less obvious).

The math is pretty easy, actually.  If you pick any two-digit number where
X is the first digit and Y is the second digit (for instance, if you pick
37, then X=3 and Y=7), then the number itself is equal to (10 times X) + Y
(by the definition of the way we write numbers), which is written 10X + Y.
The sum of the digits is X + Y.  So the answer will always be

10X + Y - (X + Y)

which is

10X + Y - X - Y

which is

9X

That is, 9 times your original tens digit.  So it's always going to be
an even multiple of 9: 9 if your original number was between 10 and 19,
18 if it was between 20 and 29, etc.

In my 37 example, the tens digit is 3 so if my algebra is right,
the answer should be 9x3=27.  And sure enough, 37 - (3+7) = 37 - 10
= 27.  Note that every time you add one to the original number, as
long as you don't hit a multiple of ten, you add one to what you're
subtracting, so the final answer is the same:

38 - (3 + 8) = 38 - 11 = 27
36 - (3 + 6) = 36 -  9 = 27
35 - (3 + 5) = 35 -  8 = 27

That's why it only changes when the tens digit changes.

-Mark
```