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Dave W.
Info Junkie
USA
26022 Posts |
 Posted - 02/17/2005 : 20:24:04 [Permalink]
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quote:
Originally posted by Ricky
Being in discrete math, I just had to try to come up with a proof for this.
***WARNGING: below contains the answer to why it works***
Let x be an integer, such that x >= 10 and x <= 99.
Therefore the first digit which make up x can be described as:
d1 = floor(x/10) (the floor of 7.3 is 7, the floor of 8.9 is 8)
[SNIP]
Let the integer y = floor(x/10) (floor must, by definition, be an integer)
You already had a representation of floor(x/10) in d1, making the last linen = 9*d1 Forget about y, the solution is that n is always 9 times the first digit of x.
Now, re-work the solution starting with d2 = x modulo 10, and don't use floor.
Dude wrote:quote:
Basically, per Ricky's solution, you get a set of numbers. The SAME symbol is assigned this entire set.
In this case, the set is 9, 18, 27, 36, 45, 54, 63, 72 and 81. Note that the same symbol is given to a few other numbers, as well, to try to hide the pattern. |
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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H. Humbert
SFN Die Hard
USA
4574 Posts |
Posted - 02/17/2005 : 20:39:51 [Permalink]
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Hmm, well not being good at math, this is what I did:
I picked their example as my number every time. Ran the program about 5 times and realized the "magic" symbol corresponded every time to the example, but that that the symbol for the example number changed every time as well!
See, I figured that by human nature, most people would probably pick a new number every time to work the calculations on, and so would find themselves with a new symbol (unsurpisingly) which the crystal ball would guess correctly (shocking). But by sticking with the same number every time I noticed more rapidly that the "list" of symbols also changed every turn, merely giving you the illusion randomly selecting a new symbol every turn. (If the symbol set was static, like on printed paper, it would become clearer much faster that the equation was always forcing you to pick a number with the same symbol over and over again.)
So, anyway, it is possible to figure out what it's doing by observing the pattern, but without necessarily figuring out the math part, which I can't do anyway. But I'm guessing that's already what most of you did.
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"A man is his own easiest dupe, for what he wishes to be true he generally believes to be true." --Demosthenes
"The first principle is that you must not fool yourself - and you are the easiest person to fool." --Richard P. Feynman
"Face facts with dignity." --found inside a fortune cookie |
| Edited by - H. Humbert on 02/17/2005 22:11:03 |
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Ricky
SFN Die Hard
USA
4907 Posts |
Posted - 02/17/2005 : 22:56:28 [Permalink]
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quote:
You already had a representation of floor(x/10) in d1, making the last line
n = 9*d1
Forget about y, the solution is that n is always 9 times the first digit of x.
While you are correct, n = 9*d1, I don't see how you got from:
d1 = floor(x/10)
To:
n (the final number) = 9 * d1
quote:
Now, re-work the solution starting with d2 = x modulo 10, and don't use floor.
Is there a reason to do this? I mean, I haven't worked it out but it seems that using modulo would have the same proof, just as long, no? There isn't really a reason not to use floor there, is there? |
Why continue? Because we must. Because we have the call. Because it is nobler to fight for rationality without winning than to give up in the face of continued defeats. Because whatever true progress humanity makes is through the rationality of the occasional individual and because any one individual we may win for the cause may do more for humanity than a hundred thousand who hug their superstitions to their breast.
- Isaac Asimov |
| Edited by - Ricky on 02/17/2005 22:57:10 |
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beskeptigal
SFN Die Hard
USA
3834 Posts |
Posted - 02/17/2005 : 23:30:07 [Permalink]
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A guy called Orsito on the Everything Science Forum posted this:quote:
It's a pretty simple equation:
(10x + y)-(x+y)=9x
If you look through the list of symbols, you will see that all multiples of 9 are the exact same symbol.
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Dave W.
Info Junkie
USA
26022 Posts |
Posted - 02/18/2005 : 19:57:25 [Permalink]
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quote:
Originally posted by Ricky
While you are correct, n = 9*d1, I don't see how you got from:
d1 = floor(x/10)
To:
n (the final number) = 9 * d1
The last few lines of your stuff were:n = 9*floor(x/10)
Let the integer y = floor(x/10) (floor must, by definition, be an integer)
n = 9*y
Thefefore the final number n must be divisible by 9. Instead of the stuff about y, you should have simply substituted d1 for floor(x/10), and then said "therefore, the final number n is nine times the first digit of the original number, always."quote:
Is there a reason to do this?
Yeah, for fun.
And yeah, Beskeptigal, that's what Ricky has, except he's got x and y represented as derived from the original number, and not as independent variables holding the first and second digits. |
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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