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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  
Newbie Joined: Nov 2010 Posts: 2 Thanks: 0  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:
 
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 1number 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 1number 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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