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Smarandache Settlement (Posted on 2014-06-24) Difficulty: 3 of 5
Determine the remainder when 1234567...404142 is divided by 43.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

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Solution computer aided solution Comment 1 of 1
Using mod 43 arithmetic all the way through, one can start with 1, and multiply by 10 or 100 as necessary, and add the new value (2 through 42) to obtain the desired answer:

after	remainder
adding
  2      12
  3 37
  4 30
  5 4
  6 3
  7 37
  8 34
  9 5
 10 37
 11 13
 12 22
 13 20
 14 36
 15 3
 16 15
 17 12
 18 14
 19 0
 20 20
 21 0
 22 22
 23 30
 24 14
 25 6
 26 24
 27 19
 28 36
 29 17
 30 10
 31 42
 32 18
 33 27
 34 25
 35 41
 36 8
 37 20
 38 17
 39 19
 40 5
 41 25
 42 5

The answer is 5.


DefDbl A-Z
Dim crlf$

Private Sub Form_Load()
 ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
 
 remainder = 1
 For i = 2 To 42
  l = Len(LTrim(Str(i)))
  remainder = (remainder * Int(10 ^ l + 0.5) + i) Mod 43
  Text1.Text = Text1.Text & Str(i) & Str(remainder) & crlf
 Next

End Sub


  Posted by Charlie on 2014-06-24 12:58:06
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