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Why Haydn ? (Posted on 2014-05-21) Difficulty: 4 of 5
WHY is the largest prime factor of HAYDN.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution | Comment 1 of 2
DefDbl A-Z
Dim   crlf$


Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 For n = 12345 To 98765
   ns$ = LTrim(Str(n))
   good = 1
   For i = 1 To 4
     If InStr(Mid(ns$, i + 1), Mid(ns$, i, 1)) > 0 Then good = 0
   Next
   If good Then
     pf = n
     While prmdiv(pf) > 1 And prmdiv(pf) < pf
      pf = pf / prmdiv(pf)
     Wend
     If pf > 99 And pf < 1000 Then
       pfs$ = LTrim(Str(pf))
       If Mid(pfs$, 2, 1) = Mid(ns$, 1, 1) And Mid(pfs$, 3, 1) = Mid(ns$, 3, 1) Then
         If InStr(ns$, Mid(pfs$, 1, 1)) = 0 Then
           Text1.Text = Text1.Text & Str(pf) & Str(n) & "     "
           n2 = n
           p = prmdiv(n2): n2 = n2 / p
           While p > 1
            Text1.Text = Text1.Text & Str(p)
            p = prmdiv(n2): n2 = n2 / p
           Wend
           Text1.Text = Text1.Text & crlf
         End If
       End If
     End If
   End If
 Next n
  Text1.Text = Text1.Text & "----------------" & crlf
  
' the following is for a similar puzzle: WHY is smallest prime factor of HAYDN.  
  
 For n = 12345 To 98765
   ns$ = LTrim(Str(n))
   good = 1
   For i = 1 To 4
     If InStr(Mid(ns$, i + 1), Mid(ns$, i, 1)) > 0 Then good = 0
   Next
   If good Then
     pf = prmdiv(n)
     If pf > 99 And pf < 1000 Then
       pfs$ = LTrim(Str(pf))
       If Mid(pfs$, 2, 1) = Mid(ns$, 1, 1) And Mid(pfs$, 3, 1) = Mid(ns$, 3, 1) Then
         If InStr(ns$, Mid(pfs$, 1, 1)) = 0 Then
           Text1.Text = Text1.Text & Str(pf) & Str(n) & "          "
           n2 = n
           p = prmdiv(n2): n2 = n2 / p
           While p > 1
            Text1.Text = Text1.Text & Str(p)
            p = prmdiv(n2): n2 = n2 / p
           Wend
           Text1.Text = Text1.Text & crlf
         End If
       End If
     End If
   End If
 Next n
  
End Sub

Function prmdiv(num)
 Dim n, dv, q
 If num = 1 Then prmdiv = 1: Exit Function
 n = Abs(num): If n > 0 Then limit = Sqr(n) Else limit = 0
 If limit <> Int(limit) Then limit = Int(limit + 1)
 dv = 2: GoSub DivideIt
 dv = 3: GoSub DivideIt
 dv = 5: GoSub DivideIt
 dv = 7
 Do Until dv > limit
   GoSub DivideIt: dv = dv + 4 '11
   GoSub DivideIt: dv = dv + 2 '13
   GoSub DivideIt: dv = dv + 4 '17
   GoSub DivideIt: dv = dv + 2 '19
   GoSub DivideIt: dv = dv + 4 '23
   GoSub DivideIt: dv = dv + 6 '29
   GoSub DivideIt: dv = dv + 2 '31
   GoSub DivideIt: dv = dv + 6 '37
 Loop
 If n > 1 Then prmdiv = n
 Exit Function

DivideIt:
 Do
  q = Int(n / dv)
  If q * dv = n And n > 0 Then
    prmdiv = dv: Exit Function
   Else
    Exit Do
  End If
 Loop

 Return
End Function

finds the following solutions to the puzzle:

 WHY HAYDN    Prime factors of HAYDN
 613 18390      2 3 5 613
 523 20397      3 13 523
 127 23749      11 17 127
 127 24765      3 5 13 127
 521 28134      2 3 3 3 521
 521 29176      2 2 2 7 521
 137 34798      2 127 137
 739 36950      2 5 5 739
 139 36974      2 7 19 139
 139 38920      2 2 2 5 7 139
 239 38957      163 239
 947 40721      43 947
 149 40975      5 5 11 149
 541 42198      2 3 13 541
 743 42351      3 19 743
 547 43760      2 2 2 2 5 547
 941 45168      2 2 2 2 3 941
 149 46935      3 3 5 7 149
 853 50327      59 853
 359 50978      2 71 359
 953 54321      3 19 953
 359 54927      3 3 17 359
 859 54976      2 2 2 2 2 2 859
 461 63157      137 461
 163 64385      5 79 163
 863 67314      2 3 13 863
 461 69150      2 3 5 5 461
 271 70189      7 37 271
 173 74390      2 5 43 173
 173 78369      3 151 173
 389 80912      2 2 2 2 13 389
 487 82790      2 5 17 487
 281 83176      2 2 2 37 281
 281 85143      3 101 281
 487 85712      2 2 2 2 11 487
 283 86315      5 61 283
 389 87914      2 113 389
 193 90324      2 2 3 3 13 193
 193 95342      2 13 19 193
 197 95742      2 3 3 3 3 3 197
 
It then finds the solution to a similar puzzle: if WHY is the smallest prime factor of HAYDN. It has only two solutions:

 157 54793           157 349
 193 96307           193 499

  Posted by Charlie on 2014-05-21 16:19:59
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