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 Lucky seven V (Posted on 2011-09-13)
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.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution | Comment 1 of 3

The digital root of z is 6.

Lines 60 through 290 of the below program are not really needed for this solution, but were added to display the digital roots also for N, x and y, which are 1, 4 and 7 respectively.

list
20   for I=1 to 2011:N=N*10+7:next
30   X=N\9
40   Y=X\9
50   Z=Y\9
60   Dr=0:Num=N
70   while Num>0
80        Dr=(Dr+Num @ 10) @ 9:Num=Num\10
90   wend:print Dr
160   Dr=0:Num=X
170   while Num>0
180        Dr=(Dr+Num @ 10) @ 9:Num=Num\10
190   wend:print Dr
260   Dr=0:Num=Y
270   while Num>0
280        Dr=(Dr+Num @ 10) @ 9:Num=Num\10
290   wend:print Dr
360   Dr=0:Num=Z
370   while Num>0
380        Dr=(Dr+Num @ 10) @ 9:Num=Num\10
390   wend:print Dr
OK
run
1
4
7
6
OK

 Posted by Charlie on 2011-09-13 13:41:33
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