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 November 18th, 2010, 11:21 AM #1 Newbie   Joined: Nov 2010 Posts: 2 Thanks: 0 Why does this apply to all tables except to a multiple of 3? What I keep wondering about is why the numbers 1 till 9 keep appearing when I do this. lets take the math table of 2 2 4 6 8 10 12 14 16 18 20 if I add the numbers until only 1 digit remains this is what happens 2 = 2 4 = 4 6 = 6 8 = 8 10 = 1+0 = 1 12 = 3 14 = 5 16 = 7 18 = 9 20 = 2 in the answer all digits 1 till 9 appear and the number in which the table comes from is the first and the last digit. The same applies for all other tables except for 3, 6 and 9 Can you explain what this mathematical problem is and why it doesn't apply to multiples of 3? for example the table of 13 13 = 4 26 = 8 39 = 12 = 3 52 = 7 65 = 11 = 2 78 = 15 = 6 91 = 10 = 1 104 = 5 117 = 9 130 = 4 To be more exact this follows exactly the same pattern as the table of 4 4 4 8 8 12 3 16 7 20 2 24 6 28 1 32 5 36 9 40 4 The multiples of 3 have this kind of pattern 3= 3 | 6= 6 6= 6 | 12= 3 9= 9 | 18= 9 12= 3 | 24= 6 15= 6 | 30= 3 18= 9 | 36= 9 21= 3 | 42= 6 24= 6 | 48= 3 27= 9 | 54= 9 30= 3 | 60= 6 and the multiples of 9 has this kind of pattern 9= 9 | 18= 9 18= 9 | 36= 9 27= 9 | 54= 9 36= 9 | 72= 9 45= 9 | 90= 9 54= 9 | 108= 9 63= 9 | 126= 9 72= 9 | 144= 9 81= 9 | 162= 9 90= 9 | 180= 9 Can someone explain this matter?
November 18th, 2010, 08:11 PM   #2
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Re: Why does this apply to all tables except to a multiple o

I've found the solution. I'm Quoting a little bit of the solution, It all comes down to the base number. In this case I used Decimals but if I used Hexadecimal I'd have gained the same but than 1 till F and as a base number, instead of 9 it would be 15 (E)

Quote:
 Originally Posted by dr Math When you repeatedly add the digits of a number until you get down to a single digit, it turns out that what you are doing (almost) is finding the remainder after dividing that number by 9. I said "almost" because if 9 divides exactly into the number, you won't get a remainder of zero; you'll get a 9 instead. This is easy to prove if you know the rules for modular arithmetic, but you can probably convince yourself by looking at a bunch of examples.

 November 19th, 2010, 07:34 AM #3 Newbie   Joined: Nov 2010 Posts: 20 Thanks: 0 Re: Why does this apply to all tables except to a multiple o I think the thing you are not realizing is: -For number 2, for example, if you take the 10 first results of the table of 2, and make them be 1-number you get every number from 0 to 9. As you have said: 0=0 2=2 4=4 6=6 8=8 10--- 1+0=1 12--- 1+2=3 14--- 1+4=5 16--- 1+6=7 18--- 1+8=9 And this happens to every number except the multiples of 3 (try with 12, for example) this happens because for a number to be multiple of 3, it MUST be 3, 6 or 9 in 1-number form. ex: 81--- 8+1=9 57--- 5+7=12 --- 1+2=3 I'm not really sure if this is what you meant, I hope this has helped you. Bye!

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