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Calculator can't handle it (Posted on 2019-05-17) Difficulty: 3 of 5
Find the sum of the digits of the number 6666....682 (The number has 105-1 6's)

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution solution Comment 1 of 1
 n = 8
 For i = 1 To 7
   n = (n - 2) * 10 + 8
   Text1.Text = Text1.Text & n & "     " & n * n & crlf
 Next
 
finds

68     4624
668     446224
6668     44462224
66668     4444622224
666668     444446222224
6666668     44444462222224
66666668     4.44444462222222E+15
 
The numbers on the left are of the form provided, and their squares appear on the right.

When there are n 6's, the square has

n 4's
one 6 
n 2's
one 4

The sum of digits is 6*n+10.

We are given n = 10^5 - 1, so the s.o.d. of the square is 6*10^5 + 4 = 600004.

  Posted by Charlie on 2019-05-17 19:25:55
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