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10 4 7 10 (Posted on 2015-11-03) Difficulty: 3 of 5
Consider decimal number 33. If converted to base 4 form it would be 201, which if regarded as 7 base number would yield 99 decimal.
Pay attention: 99=3*33.
219 is another number displaying the same feature (when converted to base 4 and interpreted as base 7 creates a multiple of the original decimal number).

Please list some additional samples.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solutions Comment 2 of 2 |
                           base 7        multiple
  base         base    interpretation       of
   10            4       in base 10      original
      1             1           1             1
      2             2           2             1
      3             3           3             1
     33           201          99             3
    219          3123        1095             5
    840         31020        7560             9
   1055        100133       16880            16
   4220       1001330      118160            28
  16880      10013300      827120            49
  95322     113101122     6958506            73
 178500     223211010    13566000            76
 714000    2232110100    94962000           133
 981540    3233220210   135452520           138
1387680   11102302200   328880160           237


DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)

 For n = 1 To 5000000
   DoEvents
   b4$ = base$(n, 4)
   b7 = fromBase(b4$, 7)
   If b7 Mod n = 0 Then
     Text1.Text = Text1.Text & mform(n, "######0") & "  " & pad(b4, 12) & mform(b7, "###########0") & mform(b7 / n, "####0") & crlf
   End If
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

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

Function fromBase(n$, b)
  v = 0
  For i = 1 To Len(n$)
    c$ = LCase$(Mid(n$, i, 1))
    If c$ > " " Then
      v = v * b + InStr("0123456789abcdefghijklmnopqrstuvwxyz", c$) - 1
    End If
  Next
  fromBase = v
End Function

Function mform$(x, t$)
  a$ = Format$(x, t$)
  If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
  mform$ = a$
End Function

Function pad$(n$, l)
  st$ = n
  If Len(st) < l Then st = Right(String(l, " ") + st, l)
  pad$ = st
End Function


  Posted by Charlie on 2015-11-03 14:31:07
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