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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! Tags apply, multiple, tables Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post eulerrules1 Computer Science 1 December 17th, 2013 09:49 AM interestedinmaths Abstract Algebra 3 December 14th, 2012 02:20 AM joekrebs Advanced Statistics 1 September 15th, 2011 07:26 PM prwells32 Advanced Statistics 4 January 30th, 2010 02:42 PM wustvn New Users 0 October 20th, 2007 10:57 PM

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