A base ten number formed by writing the digit seven precisely 2011 times is denoted by N. That is:

N = 77……77 (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.

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