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Need explanation from you mathematicians

T_R_Oglodyte

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Kay H said:
I know this must have some mathematical explanation but I don't get it but I'm math impaired. Mt DH who is very good with math problems can't figure it out either. Can anyone explain?

http://trunks.secondfoundation.org/files/psychic.sw8
Your link has an error - should be http://trunks.secondfoundation.org/files/psychic.swf

No matter what two digit number you start with, your final answer will always be 9 or a multiple of 9. The key on the right is programmed to always return the same symbol for 9 and all mulitiples of 9, and to return that symbol as the answer. The entries for all numbers that are not 9 or a multiple of 9 are totally irrelevant.

You can work it out algebraically by letting your two digit number be xy where x = any digit from 1 to 9 and y = any digit from 0 to 9. Then just follow the steps. In the end, your answer will be 9*z, where z is another digit from 1 to 9.
 
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Kay H

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Thanks, Steve. You answered me before I edited my post and corrected my link. You are fast. DH will appreciate your spped and explanation. He has been trying to figure it out for 3 days now.

Thanks again. I owe you a drink :D
 

T_R_Oglodyte

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Kay H said:
Thanks, Steve. You answered me before I edited my post and corrected my link. You are fast. DH will appreciate your spped and explanation. He has been trying to figure it out for 3 days now.

Thanks again. I owe you a drink :D
I need to expand my answer a bit. My explanation is incomplete.

Your first number actually is 10X + y. For example, if you started with 23:
  • x=2 and y=3.
  • Then, 10*x + y = 10*2 + 3 = 20 + 3 = 23.

The problem tells you to add together the two digits and subtract them from the first number.

So, algebraically what you have is:

(10x + y) - (x + y).

That rearranges to x*(10-1) + (y-y)

which simplifies to 9*x.

Thus, the final answer will be 9 mulitplied by the first digit in your two digit number.
 
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T_R_Oglodyte

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Icarus

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They had me going there for a minute, because when you click try again, the symbol table changes.

-David
 

T_R_Oglodyte

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For the more mathematically inclined, you can do the same thing with a two-digit hexadecimal number, but then the resulting answer will be a multiple of 15 instead of 9.

More generally, if you use a numbering system of base n, the resutling answer will be a multiple of n-1. This is a basic property of numbering systems. In the days before calculators, there was a procedure for checking arithmetic calculations called "casting 9's", that exploited this same property.

I was taught number bases in fifth grade, and learned to cast 9's in base 6, base 8, and base 12. Of course in those number bases, you would casts 5's, 7's, and 11's, respectively.
 

Kay H

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T_R_Oglodyte said:
I think a McMenamins Hammerhead will be a bit difficult for you to pull off. :D


Go ahead, Steve. Take advantage of a mathmatically impaired senior citizen :D :D

Actually, unbeknownst to me. DH sat down with a pencil and paper, sans math equasions and figured it out in 15 minutes before I asked here. He said I could have done the same thing (little does he know). You are waaaay too technical for my taste, but I guess I asked, didn't I.
 

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JudyS

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Ah yes -- this was posted here a year or so ago. As I recall, there were a bunch of sites out there, all with the same basic trick.

Anyway, I love the sound effect!
 
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