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Arithmetic Grid (Posted on 2014-05-30) Difficulty: 3 of 5
+----+----+----+----+
|AN  | ?? | IP | ST |
+----+----+----+----+
| ?? | ?? |??? |??? |
+----+----+----+----+
| ?? | ?? |??? |??? |
+----+----+----+----+
| ?? | ?? |PUZ |ZLE |
+----+----+----+----+
Replace each letter with a different digit in the above 4x4 grid such that:
  1. Each of the four rows and each of the four columns are in arithmetic sequence.
  2. None of the numbers can contain any leading zero.
  3. Each question mark denotes any digit whether same or different.
*** Adapted from Andrey Bogdanov, which appeared in an Internet competition.

No Solution Yet Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution Comment 1 of 1
DefDbl A-Z
Dim crlf$

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

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 DoEvents
  
 a$ = "1234567890": h$ = a$
 Do
   If Mid(a$, 1, 1) <> "0" And Mid(a$, 3, 1) <> "0" And Mid(a$, 5, 1) <> "0" And Mid(a$, 4, 1) <> "0" And Mid(a$, 8, 1) <> "0" Then
    an = Val(Mid(a$, 1, 2))
    ip = Val(Mid(a$, 3, 2))
    st = Val(Mid(a$, 5, 2))
    puz = 100 * Val(Mid(a$, 4, 1)) + Val(Mid(a$, 7, 2))
    zle = 100 * (puz Mod 10) + Val(Mid(a$, 9, 2))
    c4inc = (zle - st) / 3
    If c4inc = Int(c4inc) Then
    
        c3inc = (puz - ip) / 3
        If c3inc = Int(c3inc) Then
         r1c2 = an + st - ip
         If ip - an = 2 * (st - ip) Then
          r4inc = zle - puz
          r4c1 = puz - 2 * r4inc
          r4c2 = puz - r4inc
          c1inc = (r4c1 - an) / 3
          c2inc = (r4c2 - r1c2) / 3
          If c1inc = Int(c1inc) And c2inc = Int(c2inc) Then
            r2c1 = an + c1inc: r3c1 = r2c1 + c1inc
            r2c2 = r1c2 + c2inc: r3c2 = r2c2 + c2inc
            r2c3 = ip + c3inc: r3c3 = r2c3 + c3inc
            r2c4 = st + c4inc: r3c4 = r2c4 + c4inc
            If r2c4 - r2c3 = r2c3 - r2c2 And r2c3 - r2c2 = r2c2 - r2c1 Then
            If r3c4 - r3c3 = r3c3 - r3c2 And r3c3 - r3c2 = r3c2 - r3c1 Then
              If r4c1 > 9 And r4c2 < 100 And r2c4 > 99 Then
                    Text1.Text = Text1.Text & "ANIPSTUZLE" + crlf
                    Text1.Text = Text1.Text & a$ & crlf & crlf
                    Text1.Text = Text1.Text & mform(an, "###0") & mform(r1c2, "###0") & mform(ip, "###0") & mform(st, "###0") + crlf + crlf
                    Text1.Text = Text1.Text & mform(r2c1, "###0") & mform(r2c2, "###0") & mform(r2c3, "###0") & mform(r2c4, "###0") + crlf + crlf
                    Text1.Text = Text1.Text & mform(r3c1, "###0") & mform(r3c2, "###0") & mform(r3c3, "###0") & mform(r3c4, "###0") + crlf + crlf
                    Text1.Text = Text1.Text & mform(r4c1, "###0") & mform(r4c2, "###0") & mform(puz, "###0") & mform(zle, "###0") + crlf + crlf
                    
                    DoEvents
              End If
            End If
            End If
          End If
         End If
        End If
    
    End If
   End If
   permute a$
 Loop Until a$ = h$
 
End Sub

finds

the letter correspondences are:

ANIPSTUZLE
9581746230

and the completed grid is:

  95  88  81  74
  72  90 108 126
  49  92 135 178
  26  94 162 230


  Posted by Charlie on 2014-05-30 12:01:48
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