' Generates Inlaid Magic Squares of order 8 (Integers 1 ... 64)
' Tested with Office 2007 under Windows 7
Sub MgcSqr8k()
Dim a1(64), a(64), b1(64), b(64), c(64), s(4)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr8k")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 64: s8 = 260
For i1 = 1 To m2
a1(i1) = i1
b1(a1(i1)) = a1(i1)
Next i1
'' s(3) = 84: s(4) = 108 ''Base Case
For s3 = 15 To 93 Step 3
s(3) = s3
For s4 = 99 To 177 Step 3
s(4) = s4
s(1) = 3 * s8 / 4 - s(4): s(2) = 3 * s8 / 4 - s(3):
d = (s(4) - s(3)) / 3
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j28 = m1 To m2 ''26 To 26 'a(28)
If b(a1(j28)) = 0 Then b(a1(j28)) = a1(j28): c(28) = a1(j28) Else GoTo 280
a(28) = a1(j28)
For j27 = m1 To m2 ''8 To 8 'a(27)
If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
a(27) = a1(j27)
a(26) = s(1) - a(27) - a(28):
If a(26) < a1(m1) Or a(26) > a1(m2) Then GoTo 260:
If b1(a(26)) = 0 Then GoTo 260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(20) = 4 * s(1) / 3 - a(27) - 2 * a(28):
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 200:
If b1(a(20)) = 0 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = s(1) / 3:
If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190:
If b1(a(19)) = 0 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(18) = -2 * s(1) / 3 + a(27) + 2 * a(28):
If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180:
If b1(a(18)) = 0 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(12) = -s(1) / 3 + a(27) + a(28):
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120:
If b1(a(12)) = 0 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(11) = 2 * s(1) / 3 - a(27):
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 110:
If b1(a(11)) = 0 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(10) = 2 * s(1) / 3 - a(28):
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100:
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
''For j31 = 34 To 34 'a(31)
''If b(a1(j31)) = 0 Then b(a1(j31)) = a1(j31): c(31) = a1(j31) Else GoTo 313
''a(31) = a1(j31)
a(31) = a(28) + d
If a(31) < a1(m1) Or a(31) > a1(m2) Then GoTo 313:
If b1(a(31)) = 0 Then GoTo 313
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 313
''For j30 = 16 To 16 'a(30)
''If b(a1(j30)) = 0 Then b(a1(j30)) = a1(j30): c(30) = a1(j30) Else GoTo 300
''a(30) = a1(j30)
a(30) = a(27) + d
If a(30) < a1(m1) Or a(30) > a1(m2) Then GoTo 300:
If b1(a(30)) = 0 Then GoTo 300
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(29) = s(2) - a(30) - a(31):
If a(29) < a1(m1) Or a(29) > a1(m2) Then GoTo 290:
If b1(a(29)) = 0 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(23) = 4 * s(2) / 3 - a(30) - 2 * a(31):
If a(23) < a1(m1) Or a(23) > a1(m2) Then GoTo 230:
If b1(a(23)) = 0 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = s(2) / 3:
If a(22) < a1(m1) Or a(22) > a1(m2) Then GoTo 220:
If b1(a(22)) = 0 Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = -2 * s(2) / 3 + a(30) + 2 * a(31):
If a(21) < a1(m1) Or a(21) > a1(m2) Then GoTo 213:
If b1(a(21)) = 0 Then GoTo 213
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 213
a(15) = -s(2) / 3 + a(30) + a(31):
If a(15) < a1(m1) Or a(15) > a1(m2) Then GoTo 153:
If b1(a(15)) = 0 Then GoTo 153
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 153
a(14) = 2 * s(2) / 3 - a(30):
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140:
If b1(a(14)) = 0 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = 2 * s(2) / 3 - a(31):
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130:
If b1(a(13)) = 0 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j52 = m1 To m2 ''25 To 25 'a(52)
If b(a1(j52)) = 0 Then b(a1(j52)) = a1(j52): c(52) = a1(j52) Else GoTo 544
a(52) = a1(j52)
For j51 = m1 To m2 ''7 To 7 'a(51)
If b(a1(j51)) = 0 Then b(a1(j51)) = a1(j51): c(51) = a1(j51) Else GoTo 510
a(51) = a1(j51)
a(50) = s(3) - a(51) - a(52):
If a(50) < a1(m1) Or a(50) > a1(m2) Then GoTo 500:
If b1(a(50)) = 0 Then GoTo 500
If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
a(44) = 4 * s(3) / 3 - a(51) - 2 * a(52):
If a(44) < a1(m1) Or a(44) > a1(m2) Then GoTo 251:
If b1(a(44)) = 0 Then GoTo 251
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 251
a(43) = s(3) / 3:
If a(43) < a1(m1) Or a(43) > a1(m2) Then GoTo 430:
If b1(a(43)) = 0 Then GoTo 430
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(42) = -2 * s(3) / 3 + a(51) + 2 * a(52):
If a(42) < a1(m1) Or a(42) > a1(m2) Then GoTo 423:
If b1(a(42)) = 0 Then GoTo 423
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 423
a(36) = -s(3) / 3 + a(51) + a(52):
If a(36) < a1(m1) Or a(36) > a1(m2) Then GoTo 363:
If b1(a(36)) = 0 Then GoTo 363
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 363
a(35) = 2 * s(3) / 3 - a(51):
If a(35) < a1(m1) Or a(35) > a1(m2) Then GoTo 350:
If b1(a(35)) = 0 Then GoTo 350
If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(34) = 2 * s(3) / 3 - a(52):
If a(34) < a1(m1) Or a(34) > a1(m2) Then GoTo 361:
If b1(a(34)) = 0 Then GoTo 361
If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 361
''For j55 = 33 To 33 'a(55)
''If b(a1(j55)) = 0 Then b(a1(j55)) = a1(j55): c(55) = a1(j55) Else GoTo 547
''a(55) = a1(j55)
a(55) = a(52) + d
If a(55) < a1(m1) Or a(55) > a1(m2) Then GoTo 547:
If b1(a(55)) = 0 Then GoTo 547
If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 547
''For j54 = 15 To 15 'a(54)
''If b(a1(j54)) = 0 Then b(a1(j54)) = a1(j54): c(54) = a1(j54) Else GoTo 540
''a(54) = a1(j54)
a(54) = a(51) + d
If a(54) < a1(m1) Or a(54) > a1(m2) Then GoTo 540:
If b1(a(54)) = 0 Then GoTo 540
If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
a(53) = s(4) - a(54) - a(55):
If a(53) < a1(m1) Or a(53) > a1(m2) Then GoTo 530:
If b1(a(53)) = 0 Then GoTo 530
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(47) = 4 * s(4) / 3 - a(54) - 2 * a(55):
If a(47) < a1(m1) Or a(47) > a1(m2) Then GoTo 254:
If b1(a(47)) = 0 Then GoTo 254
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 254
a(46) = s(4) / 3:
If a(46) < a1(m1) Or a(46) > a1(m2) Then GoTo 460:
If b1(a(46)) = 0 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(45) = -2 * s(4) / 3 + a(54) + 2 * a(55):
If a(45) < a1(m1) Or a(45) > a1(m2) Then GoTo 453:
If b1(a(45)) = 0 Then GoTo 453
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 453
a(39) = -s(4) / 3 + a(54) + a(55):
If a(39) < a1(m1) Or a(39) > a1(m2) Then GoTo 393:
If b1(a(39)) = 0 Then GoTo 393
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 393
a(38) = 2 * s(4) / 3 - a(54):
If a(38) < a1(m1) Or a(38) > a1(m2) Then GoTo 383:
If b1(a(38)) = 0 Then GoTo 383
If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 383
a(37) = 2 * s(4) / 3 - a(55):
If a(37) < a1(m1) Or a(37) > a1(m2) Then GoTo 391:
If b1(a(37)) = 0 Then GoTo 391
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 391
GoSub 2000
'' n9 = n9 + 1: GoSub 645 'Print results (selected numbers)
'' n9 = n9 + 1: GoSub 650 'Print results (squares)
'' Erase b, c: GoTo 1000 'Print only first square
Erase b, c: GoTo 280 'Print only first square for selected Inner Squares and Border
3 b(c(37)) = 0: c(37) = 0
391 b(c(38)) = 0: c(38) = 0
383 b(c(39)) = 0: c(39) = 0
393 b(c(45)) = 0: c(45) = 0
453 b(c(46)) = 0: c(46) = 0
460 b(c(47)) = 0: c(47) = 0
254 b(c(53)) = 0: c(53) = 0
530 b(c(54)) = 0: c(54) = 0
540 ''Next j54
b(c(55)) = 0: c(55) = 0
547 ''Next j55
b(c(34)) = 0: c(34) = 0
361 b(c(35)) = 0: c(35) = 0
350 b(c(36)) = 0: c(36) = 0
363 b(c(42)) = 0: c(42) = 0
423 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
251 b(c(50)) = 0: c(50) = 0
500 b(c(51)) = 0: c(51) = 0
510 Next j51
b(c(52)) = 0: c(52) = 0
544 Next j52
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
153 b(c(21)) = 0: c(21) = 0
213 b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 ''Next j30
b(c(31)) = 0: c(31) = 0
313 ''Next j31
b(c(10)) = 0: c(10) = 0
100 b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 b(c(18)) = 0: c(18) = 0
180 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(26)) = 0: c(26) = 0
260 b(c(27)) = 0: c(27) = 0
270 Next j27
b(c(28)) = 0: c(28) = 0
280 Next j28
1000
Next s4
Next s3
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine MgcSqr8k")
End
' Print results (selected numbers)
645 For i1 = 1 To 64
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 9: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 9
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9 ''"MC = " + CStr(s8)
i3 = 0
For i1 = 1 To 8
For i2 = 1 To 8
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
2000 fl1 = 0
For j64 = m1 To m2 'a(64)
If b(a1(j64)) = 0 Then b(a1(j64)) = a1(j64): c(64) = a1(j64) Else GoTo 640
a(64) = a1(j64)
a(1) = s8 / 4 - a(64): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j63 = m1 To m2 'a(63)
If b(a1(j63)) = 0 Then b(a1(j63)) = a1(j63): c(63) = a1(j63) Else GoTo 630
a(63) = a1(j63)
a(58) = a(63) - s(3) + s(4)
If a(58) < a1(m1) Or a(58) > a1(m2) Then GoTo 580
If b1(a(58)) = 0 Then GoTo 580
If b(a(58)) = 0 Then b(a(58)) = a(58): c(58) = a(58) Else GoTo 580
a(7) = s8 / 4 - a(63) + s(3) - s(4)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(2) = s8 / 4 - a(63): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j62 = m1 To m2 'a(62)
If b(a1(j62)) = 0 Then b(a1(j62)) = a1(j62): c(62) = a1(j62) Else GoTo 620
a(62) = a1(j62)
a(59) = a(62) - s(3) + s(4)
If a(59) < a1(m1) Or a(59) > a1(m2) Then GoTo 590
If b1(a(59)) = 0 Then GoTo 590
If b(a(59)) = 0 Then b(a(59)) = a(59): c(59) = a(59) Else GoTo 590
a(6) = s8 / 4 - a(62) + s(3) - s(4)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(3) = s8 / 4 - a(62): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j61 = m1 To m2 'a(61)
If b(a1(j61)) = 0 Then b(a1(j61)) = a1(j61): c(61) = a1(j61) Else GoTo 610
a(61) = a1(j61)
a(60) = a(61) - s(3) + s(4)
If a(60) < a1(m1) Or a(60) > a1(m2) Then GoTo 600
If b1(a(60)) = 0 Then GoTo 600
If b(a(60)) = 0 Then b(a(60)) = a(60): c(60) = a(60) Else GoTo 600
a(57) = s8 - 2 * a(61) - 2 * a(62) - 2 * a(63) - a(64) + 3 * s(3) - 3 * s(4)
If a(57) < a1(m1) Or a(57) > a1(m2) Then GoTo 570
If b1(a(57)) = 0 Then GoTo 570
If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570
a(8) = s8 / 4 - a(57): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(5) = s8 / 4 - a(61) + s(3) - s(4)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(4) = s8 / 4 - a(61): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j56 = m1 To m2 'a(56)
If b(a1(j56)) = 0 Then b(a1(j56)) = a1(j56): c(56) = a1(j56) Else GoTo 560
a(56) = a1(j56)
a(49) = s8 - a(56) - s(3) - s(4)
If a(49) < a1(m1) Or a(49) > a1(m2) Then GoTo 490
If b1(a(49)) = 0 Then GoTo 490
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
a(16) = -3 * s8 / 4 + a(56) + s(3) + s(4)
If a(16) < a1(m1) Or a(16) > a1(m2) Then GoTo 160
If b1(a(16)) = 0 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(9) = s8 / 4 - a(56): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j48 = m1 To m2 'a(48)
If b(a1(j48)) = 0 Then b(a1(j48)) = a1(j48): c(48) = a1(j48) Else GoTo 480
a(48) = a1(j48)
a(41) = s8 - a(48) - s(3) - s(4)
If a(41) < a1(m1) Or a(41) > a1(m2) Then GoTo 410
If b1(a(41)) = 0 Then GoTo 410
If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(40) = 2 * s8 - a(48) - a(56) - a(61) - a(62) - a(63) - a(64) - 3 * s(4)
If a(40) < a1(m1) Or a(40) > a1(m2) Then GoTo 400
If b1(a(40)) = 0 Then GoTo 400
If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(33) = s8 - a(40) - s(3) - s(4)
If a(33) < a1(m1) Or a(33) > a1(m2) Then GoTo 330
If b1(a(33)) = 0 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(32) = s8 / 4 - a(33): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(25) = -s8 / 2 - a(32) + s(3) + s(4)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(24) = -3 * s8 / 4 + a(48) + s(3) + s(4)
If a(24) < a1(m1) Or a(24) > a1(m2) Then GoTo 240
If b1(a(24)) = 0 Then GoTo 240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(17) = s8 / 4 - a(48): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
' n9 = n9 + 1: GoSub 645 'Print results (selected numbers)
n9 = n9 + 1: GoSub 650 'Print results (squares)
Return 'Print only first Border for Selected Inner squares
b(c(17)) = 0: c(17) = 0
170 b(c(24)) = 0: c(24) = 0
240 b(c(25)) = 0: c(25) = 0
250 b(c(32)) = 0: c(32) = 0
320 b(c(33)) = 0: c(33) = 0
330 b(c(40)) = 0: c(40) = 0
400 b(c(41)) = 0: c(41) = 0
410 b(c(48)) = 0: c(48) = 0
480 Next j48
b(c(9)) = 0: c(9) = 0
90 b(c(16)) = 0: c(16) = 0
160 b(c(49)) = 0: c(49) = 0
490 b(c(56)) = 0: c(56) = 0
560 Next j56
b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(8)) = 0: c(8) = 0
80 b(c(57)) = 0: c(57) = 0
570 b(c(60)) = 0: c(60) = 0
600 b(c(61)) = 0: c(61) = 0
610 Next j61
b(c(3)) = 0: c(3) = 0
30 b(c(6)) = 0: c(6) = 0
60 b(c(59)) = 0: c(59) = 0
590 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(2)) = 0: c(2) = 0
20 b(c(7)) = 0: c(7) = 0
70 b(c(58)) = 0: c(58) = 0
580 b(c(63)) = 0: c(63) = 0
630 Next j63
b(c(1)) = 0: c(1) = 0
10 b(c(64)) = 0: c(64) = 0
640 Next j64
Return
End Sub
