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Pandigitals Divided by 11 (Posted on 2017-07-23) Difficulty: 3 of 5
For which bases b is it possible to make a pandigital number in base b that is divisible by 11 in base b?

For example, in base 4: 1023 / 11 = 33. (In base 10 this is 75 / 5 = 15.)

No Solution Yet Submitted by Brian Smith    
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Some Thoughts computer exploration | Comment 1 of 4
dividend and quotient
in the given bases:

1023  33
10324  434
120435  10545
10234576  730416
102347586  8304326
1024375869  93125079

are such pandigitals in bases 4, 5, 6, 8, 9 and 10.

There are others in these bases, but these were the first found for each of those bases.

It doesn't tell me much. Base 7 is missing. When we go higher than base 10, execution time is too long.

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For b = 3 To 30
   dvsr = b + 1
   low = Int(b ^ (b - 1))
   high = Int(b ^ b - 1)
   mlt = Int(low / dvsr)
   Do
     found = 0
     prod = dvsr * mlt
     inbase$ = base$(prod, b)
     If Len(inbase$) = b Then
       good = 1
       For i = 2 To Len(inbase)
         If InStr(inbase, Mid(inbase, i, 1)) < i Then good = 0: Exit For
       Next
       If good Then
         Text1.Text = Text1.Text & inbase & "  " & base$(mlt, b) & crlf
         found = 1: Exit Do
       End If
     End If
     mlt = mlt + 1
     DoEvents
   Loop Until prod > high
 Next
 
 
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

Function base$(n, b)
  v$ = ""
  n2 = n
  Do
    q = Int(n2 / b)
    d = n2 - q * b
    n2 = q
   ' d = n2 Mod b
   ' n2 = n2 \ b
    v$ = Mid("0123456789abcdefghijklmnopqrstuvwxyz", d + 1, 1) + v$
  Loop Until n2 = 0
  base$ = v$
End Function


  Posted by Charlie on 2017-07-23 10:39:48
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