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 2+2=4 is true (Posted on 2014-06-22)
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 No Rating

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 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\$

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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