369 pattern when you add multiples 0f 3 digits up?

Answer 1

Draw 3 columns on a sheet of paper. At the top of the first column, put the number 3. Put the number 6 at the top of the second column and 9 at the top of the third column. These numbers (3, 6, and 9) are the first 3 multiples of 3.

Now, starting with the first column (the one with the 3 at the top) put the number 12 (the next multiple of 3) below the number 3 (the last number in that column). So, in the first column you will have 3 at the top and then a 12 right below it. Move on to the next column and add the next multiple of 3 (in this case, 15) below the last number in that column (in this case, 6). Keep doing this until you reach the number 45. (Really you can continue for as long as you like, but for the purposes of this description, I am stopping there.)


Now, you should have three columns containing numbers that when read top to bottom, and left to right will be Column1: 3, 12, 21, 30, 39; Column2: 6, 15, 24, 33, 42; Column3: 9, 18, 27, 36, 45.


The interesting thing about these numbers is that when you add up the integers that make up the numbers until it is reduced down to a single digit, the resulting number will be the number at the top of the column. For example, the values in Column one were 3, 12, 21, 30, and 39. So, lets start with 12. If you add the integers that make up 12 (namely 1 and 2) you get 3. Continuing with the rest of the numbers in the column we get: 2+1 = 3, 3+0 = 3. When you get to 39 it gets a little more tricky, because you have to add the integers together twice. For example, 3+9 = 12, but as we learned about 12 earlier 1+2 = 3.


The same is true of the other two columns as well. This should not be surprising to those familiar with the fact that the integers that make up the multiples of 9, when added together, result in the number 9.


So, now you know the secret. Impress your friends. Confirm your nerdiness!