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 The magnificent twelve (Posted on 2017-04-07)
Z+E+R+O = 0
O+N+E = 1
T+W+O = 2
T+H+R+E+E = 3
F+O+U+R = 4
F+I+V+E = 5
S+I+X = 6
S+E+V+E+N = 7
E+I+G+H+T = 8
N+I+N+E = 9
T+E+N = 10
E+L+E+V+E+N =11
T+W+E+L+V+E = 12

Solve the above system of alphametics, allowing non-zero integers, whose absolute value does not exceed 11.

Rem 1: The source will be disclosed with the official solution.
Rem 2: An analytical solution (d4) will be applauded!

 See The Solution Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer solution (spoiler) -- with a caveat on the restrictions | Comment 1 of 3
Allowing duplicates, as in simultatneous equations, would allow multiple solutions. Since this is an alphametic, duplicates can't be allowed. But when that restriction was added, there were no solutions found.

But then I thought: what if the restriction against value zero did not apply to the letter O. That leads to a unique solution:

` Z E R O N T W  H F U I V S X G L-6-1 7 0 2 9-7-11-4 1 6 4 3-3 5 8`
`-6-1 7 0          0 0 2-1            1 9-7 0            2 9-11 7-1-1       3-4 0 1 7          4-4 6 4-1          5 3 6-3            6 3-1 4-1 2        7-1 6 5-11 9       8 2 6 2-1          9 9-1 2           10-1 8-1 4-1 2     11 9-7-1 8 4-1     12`

Dim crlf\$

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

maxallow = 11

For w = -maxallow To maxallow Step 2
o = (-7 - w) / 2
If Abs(o) <= maxallow Then
t = o + 9            'two
If t <= maxallow And t <> 0 Then
'    Text1.Text = "T W O = " & Str(t) & Str(w) & Str(o) & crlf
For e = -maxallow To maxallow
If e <> 0 Then     'ten
n = 10 - t - e
If Abs(n) <= maxallow And n <> 0 Then
i = 9 - 2 * n - e               'nine
If Abs(i) <= maxallow And i <> 0 Then
For s = -maxallow To maxallow          ' seven
If s <> 0 Then
v = 7 - 2 * e - n - s
If Abs(v) <= maxallow And v <> 0 Then
l = 12 - 2 * e - v - t - w          'twelve
If Abs(l) <= maxallow And l <> 0 Then
For z = -maxallow To maxallow
If z <> 0 Then
r = -z - e - o                   'zero
If Abs(r) <= maxallow And r <> 0 Then
For f = -maxallow To maxallow
If f <> 0 Then
u = 4 - o - f - r             'four
If Abs(u) <= maxallow And u <> 0 Then
h = 3 - t - r - 2 * e          'three
If Abs(h) <= maxallow And h <> 0 Then
x = 6 - s - i                  'six
If Abs(x) <= maxallow And x <> 0 Then
g = 8 - e - i - h - t           'eight
If Abs(g) <= maxallow And g <> 0 Then

If o + n + e = 1 Then
If e + l + e + v + e + n = 11 Then
If f + i + v + e = 5 Then
If z <> e And z <> r And z <> o And z <> n And z <> t And z <> w And z <> h And z <> f And z <> u And z <> i And z <> v And z <> s And z <> x And z <> x And z <> l Then
If e <> r And e <> o And e <> n And e <> t And e <> w And e <> h And e <> f And e <> u And e <> i And e <> v And e <> s And e <> x And e <> x And e <> l Then
If r <> o And r <> n And r <> t And r <> w And r <> h And r <> f And r <> u And r <> i And r <> v And r <> s And r <> x And r <> x And r <> l Then
If o <> n And o <> t And o <> w And o <> h And o <> f And o <> u And o <> i And o <> v And o <> s And o <> x And o <> x And o <> l Then
If n <> t And n <> w And n <> h And n <> f And n <> u And n <> i And n <> v And n <> s And n <> x And n <> x And n <> l Then
If t <> w And t <> h And t <> f And t <> u And t <> i And t <> v And t <> s And t <> x And t <> x And t <> l Then
If w <> h And w <> f And w <> u And w <> i And w <> v And w <> s And w <> x And w <> x And w <> l Then
If h <> f And h <> u And h <> i And h <> v And h <> s And h <> x And h <> x And h <> l Then
If f <> u And f <> i And f <> v And f <> s And f <> x And f <> x And f <> l Then
If u <> i And u <> v And u <> s And u <> x And u <> x And u <> l Then
If i <> v And i <> s And i <> x And i <> x And i <> l Then
If v <> s And v <> x And v <> x And v <> l Then
If s <> x And s <> x And s <> l Then
If g <> z And g <> e And g <> r And g <> o And g <> n And g <> t And g <> w And g <> h And g <> f And g <> u And g <> i And g <> v And g <> s And g <> x And g <> x And g <> l Then

If x <> l Then
Text1.Text = Text1.Text & Str(z) & Str(e) & Str(r) & Str(o) & Str(n) & Str(t) & Str(w) & Str(h) & Str(f) & Str(u) & Str(i) & Str(v) & Str(s) & Str(x) & Str(g) & Str(l) & crlf
Text1.Text = Text1.Text & Str(z) & Str(e) & Str(r) & Str(o)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & z + e + r + o & crlf
Text1.Text = Text1.Text & Str(o) & Str(n) & Str(e)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & o + n + e & crlf
Text1.Text = Text1.Text & Str(t) & Str(w) & Str(o)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & t + w + o & crlf
Text1.Text = Text1.Text & Str(t) & Str(h) & Str(r) & Str(e) & Str(e)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & t + h + r + e + e & crlf
Text1.Text = Text1.Text & Str(f) & Str(o) & Str(u) & Str(r)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & f + o + u + r & crlf
Text1.Text = Text1.Text & Str(f) & Str(i) & Str(v) & Str(e)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & f + i + v + e & crlf
Text1.Text = Text1.Text & Str(s) & Str(i) & Str(x)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & s + i + x & crlf
Text1.Text = Text1.Text & Str(s) & Str(e) & Str(v) & Str(e) & Str(n)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & s + e + v + e + n & crlf
Text1.Text = Text1.Text & Str(e) & Str(i) & Str(g) & Str(h) & Str(t)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & e + i + g + h + t & crlf
Text1.Text = Text1.Text & Str(n) & Str(i) & Str(n) & Str(e)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & n + i + n + e & crlf
Text1.Text = Text1.Text & Str(t) & Str(e) & Str(n)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & t + e + n & crlf
Text1.Text = Text1.Text & Str(e) & Str(l) & Str(e) & Str(v) & Str(e) & Str(n)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & e + l + e + v + e + n & crlf
Text1.Text = Text1.Text & Str(t) & Str(w) & Str(e) & Str(l) & Str(v) & Str(e)
Text1.Text = Text1.Text & "     "
Text1.Text = Text1.Text & t + w + e + l + v + e & crlf & crlf
DoEvents
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If
End If 'eleven
End If 'one

End If
End If
End If
End If
End If
Next
End If
End If
Next
End If
End If
End If
Next
End If
End If
End If
Next
End If
End If
Next w

Text1.Text = Text1.Text & crlf & ways & " done"

End Sub

Edited on April 7, 2017, 3:53 pm
 Posted by Charlie on 2017-04-07 12:26:51

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