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 Arithmetic Grid (Posted on 2014-05-30)
```+----+----+----+----+
|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)

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 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

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:

`ANIPSTUZLE9581746230`

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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