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.