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2+2=4 is true (Posted on 2014-06-22) Difficulty: 3 of 5
In what bases the cryptarithmetic puzzle TOO + TOO = FOR has a unique solution?

case A: each letter could be any digit, including 0.
case B: T could be any digit, except 0.
.

No Solution Yet Submitted by Ady TZIDON    
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Solution computer solutions Comment 2 of 2 |
For the first and second parts (above and below dashed line), each group shows the base, then the addition in that base, and then the decimal equivalents of the numbers shown:

 4
33+33=132
 15 15 30

 5
44+44=143
 24 24 48

------------
 6
155+155=354
 71 71 142

 7
166+166=365
 97 97 194

In the part-1 instances, T is the leading zero and doesn't show up in the printing.

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
 For b = 2 To 50
   For showflag = 0 To 1
    Text2.Text = Str(b)
    DoEvents
    solct = 0
    ReDim used(b - 1)
    For t = 0 To b - 1
     used(t) = 1
    For o = 0 To b - 1
     If used(o) = 0 Then
        used(o) = 1
        too = b * b * t + o * (b + 1)
    For f = 0 To b - 1
     If used(f) = 0 Then
        used(f) = 1
    For r = 0 To b - 1
     If used(r) = 0 Then
        used(r) = 1
        forval = f * b * b + o * b + r
        
        If too + too = forval Then
         solct = solct + 1
         If showflag Then Text1.Text = Text1.Text & base$(too, b) & "+" & base$(too, b) & "=" & base$(forval, b) & crlf
         If showflag Then Text1.Text = Text1.Text & Str(too) & Str(too) & Str(forval) & crlf & crlf
        End If
        
        used(r) = 0
     End If
    Next
        used(f) = 0
     End If
    Next
        used(o) = 0
     End If
    Next
     used(t) = 0
    Next
    If solct = 1 And showflag = 0 Then
     Text1.Text = Text1.Text & Str(b) & crlf
     DoEvents
    Else
     Exit For  ' showflag
    End If
   Next showflag
 Next b

Text1.Text = Text1.Text & "------------" & crlf

 For b = 2 To 50
   For showflag = 0 To 1
    Text2.Text = Str(b)
    DoEvents
    solct = 0
    ReDim used(b - 1)
    For t = 1 To b - 1
     used(t) = 1
    For o = 0 To b - 1
     If used(o) = 0 Then
        used(o) = 1
        too = b * b * t + o * (b + 1)
    For f = 0 To b - 1
     If used(f) = 0 Then
        used(f) = 1
    For r = 0 To b - 1
     If used(r) = 0 Then
        used(r) = 1
        forval = f * b * b + o * b + r
        
        If too + too = forval Then
         solct = solct + 1
         If showflag Then Text1.Text = Text1.Text & base$(too, b) & "+" & base$(too, b) & "=" & base$(forval, b) & crlf
         If showflag Then Text1.Text = Text1.Text & Str(too) & Str(too) & Str(forval) & crlf & crlf
        End If
        
        used(r) = 0
     End If
    Next
        used(f) = 0
     End If
    Next
        used(o) = 0
     End If
    Next
     used(t) = 0
    Next
    If solct = 1 And showflag = 0 Then
     Text1.Text = Text1.Text & Str(b) & crlf
     DoEvents
    Else
     Exit For  ' showflag
    End If
   Next showflag
 Next b

End Sub
Function base$(n, b)
  v$ = ""
  n2 = n
  Do
    d = n2 Mod b
    n2 = n2 \ b
    v$ = LTrim(Str(d)) + v$
  Loop Until n2 = 0
  base$ = v$
End Function



  Posted by Charlie on 2014-06-22 13:07:40
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