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Straight or rotated (Posted on 2017-08-10) Difficulty: 3 of 5
ABC + DEF = GHI
GDA + HEB = IFC

There are two sets of simultaneous solutions for the above 2 alphametics,
one being a 90o rotation of the other.

Find both.

No leading zeroes.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution program and solution (spoilers) | Comment 1 of 3
The program below prints GHI first and ABC last so that GDA, etc. read correctly downward.

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 s$ = "1234567890": h$ = s
 Do
   abc = Val(Mid(s, 1, 3))
   def = Val(Mid(s, 4, 3))
   ghi = Val(Mid(s, 7, 3))
   gda = 100 * Val(Mid(s, 7, 1)) + 10 * Val(Mid(s, 4, 1)) + Val(Mid(s, 1, 1))
   heb = 100 * Val(Mid(s, 8, 1)) + 10 * Val(Mid(s, 5, 1)) + Val(Mid(s, 2, 1))
   ifc = 100 * Val(Mid(s, 9, 1)) + 10 * Val(Mid(s, 6, 1)) + Val(Mid(s, 3, 1))
   If abc + def = ghi Then
   If gda + heb = ifc Then
   If abc > 100 And def > 100 And gda > 100 And heb > 100 Then
      Text1.Text = Text1.Text & ghi & crlf & def & crlf & abc & crlf & crlf
   End If
   End If
   End If
   permute s
   DoEvents
 Loop Until s = h
 
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub


produces

639
157
482

729
146
583




Annotated:

639 ghi
157 def
482 abc

729 ghi
146 def
583 abc

They do not seem to be rotations of each other, although digits that shared a column now share a row and vice versa.


  Posted by Charlie on 2017-08-10 11:16:22
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