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Lucky seven V (Posted on 2011-09-13) Difficulty: 3 of 5
A base ten number formed by writing the digit seven precisely 2011 times is denoted by N. That is:

N = 7777 (2011 times).

Let us denote x = [N/9], y = [x/9] and, z = [y/9]

Determine the digital root of z.

Note: [P] denotes the greatest integer ≤ P

**** For an extra challenge, solve this puzzle without using a computer program.

No Solution Yet Submitted by K Sengupta    
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Question Outline of non-computer solution | Comment 2 of 3 |
First of all z = [N/729] so you really don't need x and y.

Take the decimal for 1/729 it is a repeating decimal the repeats every 81 digits.  Find the sum of these digits.  

z will be a 2009 digit number which is which is 24*84+65 so multiply the above sum by 24 and add in the first 65 digits of the decimal of 1/729.  Covert this to a digital root

Im getting a little lost here.  I think you can just multiply this result by the digital root of 7777 which is 1.


  Posted by Jer on 2011-09-14 11:03:47
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