' Generates Magic Squares of order 6 for distict integers (Main Diagonals)
' Tested with Office 2007 under Windows 7
Sub MgcSqr6a()
Dim a(36), b(36), c(36)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr6a")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 36: s1 = 111
' Generate data
Sheets("Klad1").Select
t1 = Timer
'Row 1
For j36 = 1 To 1 ''m1 To m2 'a(36)
If b(j36) = 0 Then b(j36) = j36: c(36) = j36 Else GoTo 360
a(36) = j36
For j35 = 35 To 35 ''m2 To m1 Step -1 'a(35)
If b(j35) = 0 Then b(j35) = j35: c(35) = j35 Else GoTo 350
a(35) = j35
For j34 = 34 To 34 ''m2 To m1 Step -1 'a(34)
If b(j34) = 0 Then b(j34) = j34: c(34) = j34 Else GoTo 340
a(34) = j34
For j33 = 3 To 3 ''m1 To m2 'a(33)
If b(j33) = 0 Then b(j33) = j33: c(33) = j33 Else GoTo 330
a(33) = j33
For j32 = 32 To 32 ''m1 To m2 'a(32)
If b(j32) = 0 Then b(j32) = j32: c(32) = j32 Else GoTo 320
a(32) = j32
a(31) = s1 - a(32) - a(33) - a(34) - a(35) - a(36)
If a(31) <= 0 Or a(31) > 36 Then GoTo 310
If a(31) < a(36) Then GoTo 310 ' Ess Diff
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
'Diagonal 1
For j29 = 8 To 8 ''j36 + 1 To m2 'a(29) Ess Siff
If b(j29) = 0 Then b(j29) = j29: c(29) = j29 Else GoTo 290
a(29) = j29
For j22 = 15 To 15 ''j29 + 1 To m2 'a(22) Ess Diff
If b(j22) = 0 Then b(j22) = j22: c(22) = j22 Else GoTo 220
a(22) = j22
For j15 = 22 To 22 ''j22 + 1 To m2 'a(15) Ess Diff
If b(j15) = 0 Then b(j15) = j15: c(15) = j15 Else GoTo 150
a(15) = j15
For j8 = 29 To 29 ''j29 + 1 To m2 'a(8) Ess Diff
If b(j8) = 0 Then b(j8) = j8: c(8) = j8 Else GoTo 80
a(8) = j8
a(1) = s1 - a(8) - a(15) - a(22) - a(29) - a(36)
If a(1) <= 0 Or a(1) > 36 Then GoTo 10
If a(1) < a(36) Then GoTo 10 ' Ess Diff
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
'Column 2
For j23 = 23 To 23 ''m1 To m2 'a(23)
If b(j23) = 0 Then b(j23) = j23: c(23) = j23 Else GoTo 230
a(23) = j23
For j17 = 17 To 17 ''m1 To m2 'a(17)
If b(j17) = 0 Then b(j17) = j17: c(17) = j17 Else GoTo 170
a(17) = j17
For j11 = 26 To 26 ''j36 + 1 To m2 'a(11) Ess Diff
If b(j11) = 0 Then b(j11) = j11: c(11) = j11 Else GoTo 110
a(11) = j11
a(5) = s1 - a(11) - a(17) - a(23) - a(29) - a(35)
If a(5) <= 0 Or a(5) > 36 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
'Diagonal 2
For j26 = j36 + 1 To m2 'a(26) Ess Diff
If b(j26) = 0 Then b(j26) = j26: c(26) = j26 Else GoTo 260
a(26) = j26
For j21 = j36 + 1 To m2 'a(21) Ess Diff
If b(j21) = 0 Then b(j21) = j21: c(21) = j21 Else GoTo 210
a(21) = j21
For j16 = j36 + 1 To m2 'a(16) Ess Diff
If b(j16) = 0 Then b(j16) = j16: c(16) = j16 Else GoTo 160
a(16) = j16
a(6) = s1 - a(11) - a(16) - a(21) - a(26) - a(31)
If a(6) <= 0 Or a(6) > 36 Then GoTo 60
If a(6) < a(36) Then GoTo 60 ' Ess Diff
If a(6) < a(31) Then GoTo 60 ' Ess Diff
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
'Column 5
For j20 = m1 To m2 'a(20)
If b(j20) = 0 Then b(j20) = j20: c(20) = j20 Else GoTo 200
a(20) = j20
For j14 = m1 To m2 'a(14)
If b(j14) = 0 Then b(j14) = j14: c(14) = j14 Else GoTo 140
a(14) = j14
a(2) = s1 - a(8) - a(14) - a(20) - a(26) - a(32)
If a(2) <= 0 Or a(2) > 36 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
'Row 6
For j3 = m1 To m2 'a(3)
If b(j3) = 0 Then b(j3) = j3: c(3) = j3 Else GoTo 30
a(3) = j3
a(4) = s1 - a(1) - a(2) - a(3) - a(5) - a(6)
If a(4) <= 0 Or a(4) > 36 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
'Column 3
For j28 = m1 To m2 'a(28)
If b(j28) = 0 Then b(j28) = j28: c(28) = j28 Else GoTo 280
a(28) = j28
a(10) = s1 - a(4) - a(16) - a(22) - a(28) - a(34)
If a(10) <= 0 Or a(10) > 36 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
'Column 4
For j27 = m1 To m2 'a(27)
If b(j27) = 0 Then b(j27) = j27: c(27) = j27 Else GoTo 270
a(27) = j27
a(9) = s1 - a(3) - a(15) - a(21) - a(27) - a(33)
If a(9) <= 0 Or a(9) > 36 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
'Row 3
For j24 = m1 To m2 'a(24)
If b(j24) = 0 Then b(j24) = j24: c(24) = j24 Else GoTo 240
a(24) = j24
a(19) = s1 - a(20) - a(21) - a(22) - a(23) - a(24)
If a(19) <= 0 Or a(19) > 36 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
'Row 4
For j18 = m1 To m2 'a(18)
If b(j18) = 0 Then b(j18) = j18: c(18) = j18 Else GoTo 180
a(18) = j18
a(13) = s1 - a(14) - a(15) - a(16) - a(17) - a(18)
If a(13) <= 0 Or a(13) > 36 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
'Remainder
For j12 = m1 To m2 'a(12)
If b(j12) = 0 Then b(j12) = j12: c(12) = j12 Else GoTo 120
a(12) = j12
a(7) = s1 - a(8) - a(9) - a(10) - a(11) - a(12)
If a(7) <= 0 Or a(7) > 36 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(25) = s1 - a(1) - a(7) - a(13) - a(19) - a(31)
If a(25) <= 0 Or a(25) > 36 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(30) = s1 - a(12) - a(18) - a(24) - a(6) - a(36)
If a(30) <= 0 Or a(30) > 36 Then GoTo 300
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
5
b(c(30)) = 0: c(30) = 0
300 b(c(25)) = 0: c(25) = 0
250 b(c(7)) = 0: c(7) = 0
70 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(13)) = 0: c(13) = 0
130 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(19)) = 0: c(19) = 0
190 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(9)) = 0: c(9) = 0
90 b(c(27)) = 0: c(27) = 0
270 Next j27
b(c(10)) = 0: c(10) = 0
100 b(c(28)) = 0: c(28) = 0
280 Next j28
b(c(4)) = 0: c(4) = 0
40 b(c(3)) = 0: c(3) = 0
30 Next j3
b(c(2)) = 0: c(2) = 0
20 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(6)) = 0: c(6) = 0
60 b(c(16)) = 0: c(16) = 0
160 Next j16
b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(5)) = 0: c(5) = 0
50 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(1)) = 0: c(1) = 0
10 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(29)) = 0: c(29) = 0
290 Next j29
b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(36)) = 0: c(36) = 0
360 Next j36
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Combinations"
y = MsgBox(t10, 0, "Routine MgcSqr6a")
End
Return
' Print results (selected numbers)
640 For i1 = 1 To 36
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 6 Then
n2 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 36
a2 = a(j1)
For j2 = (1 + j1) To 36
If a2 = a(j2) Then fl1 = 0: GoTo 850
Next j2
Next j1
850 Return
End Sub
