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The 73rd digit (Posted on 2013-01-29) Difficulty: 3 of 5
a = 111...111 (a string of 2012 ones)

What is the 73rd digit from the end of a2?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Solution with D1 explanation Comment 3 of 3 |
If you were to do out the long multiplication of a*a
the last digit would be 1
the second to last digit would be 1+1 = 2
the third to last digits would be 1+1+1 = 3
the nth to last digit would be the last digit of n plus any carries

the 73rd digit would be 3 plus a 7 carried from the 72nd digit.  There would almost be another 1 carried from the 71st digit but the 72nd digit is just 2 plus 7.  So the solution is 0.

The 74th digit would end as 7 plus 4 plus the extra 1 carried up from the 7 plus 3 at the 73rd place.  This is the first extra carry so the few digits beginning with the 74th are
2098765432...

  Posted by Jer on 2013-01-29 12:22:18
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