Radio Astronomy Systems Research Group

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=====Answer:=====

There are two ways of solving this. For a pretty thorough explanation of the first check out this video: http://www.youtube.com/watch?v=Dd81F6-Ar_0 

Here is a brief explanation of both.

==Method 1==

Similar to the Gauss question, add up the digits in each pair of numbers.
  0 1 2 3 ... 999996 999997 999998 999999 1000000
  ^                                   ^ 
  0 1 2 3 ... 999996 999997 999998 999999 1000000
    ^                         ^ 
  0 1 2 3 ... 999996 999997 999998 999999 1000000
      ^                ^ 
  0 1 2 3 ... 999996 999997 999998 999999 1000000
        ^        ^ 
    etc.

  0 + 999999 = 999999
  1 + 999998 = 999999
  2 + 999997 = 999999
  ....
Now you have 500000 pairs that sum up to 999999
  500000 * (9 + 9 + 9 + 9 + 9 + 9) = 27000000
Don't forget 1 million!
  27000000 + 1 + 0 + 0 + 0 + 0 + 0 + 0 = 27000001

==Method 2==
  
Write each number using 6 digits (i.e. zero extend)

  000001
  000002
  000003
  ...
  999999
  
Each digit shows up in each column 100000 times. The sum of the digits 1-9 is 45.
  45*100000*6 = 27000000
Plus that last 1 in 1 million
  27000000 + 1 = 27000001

Radio Astronomy Systems Research Group

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