' Generates Magic Squares of order 8, Magic Sum 260, (Magic Sub Squares, Magic Middle Squares)
' Tested with Office 2007 under Windows 7
Sub MgcSqr8d2()
Dim a(64), b(64), c(64)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr8d2")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 64: s1 = 260
' Generate data
Sheets("Klad1").Select
t1 = Timer
For j64 = m1 To m2 'a(64) = 55
If b(j64) = 0 Then b(j64) = j64: c(64) = j64 Else GoTo 640
a(64) = j64
For j63 = m1 To m2 'a(63) = 29
If b(j63) = 0 Then b(j63) = j63: c(63) = j63 Else GoTo 630
a(63) = j63
For j62 = m1 To m2 'a(62) = 34
If b(j62) = 0 Then b(j62) = j62: c(62) = j62 Else GoTo 620
a(62) = j62
a(61) = 0.5 * s1 - a(62) - a(63) - a(64)
If a(61) < m1 Or a(61) > m2 Then GoTo 610
If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610
For j60 = m1 To m2 'a(60) = 23
If b(j60) = 0 Then b(j60) = j60: c(60) = j60 Else GoTo 600
a(60) = j60
a(59) = 0.5 * s1 - a(60) - a(61) - a(62)
If a(59) < m1 Or a(59) > m2 Then GoTo 590
If b(a(59)) = 0 Then b(a(59)) = a(59): c(59) = a(59) Else GoTo 590
For j58 = m1 To m2 'a(58) = 2
If b(j58) = 0 Then b(j58) = j58: c(58) = j58 Else GoTo 580
a(58) = j58
a(57) = -a(58) + a(61) + a(62): If a(57) < m1 Or a(57) > m2 Then GoTo 570:
If b(a(57)) = 0 Then b(a(57)) = a(57): c(57) = a(57) Else GoTo 570
a(56) = -0.25 * s1 + a(61) + a(62) + a(64): If a(56) < m1 Or a(56) > m2 Then GoTo 560:
If b(a(56)) = 0 Then b(a(56)) = a(56): c(56) = a(56) Else GoTo 560
a(55) = 0.25 * s1 - a(64): If a(55) < m1 Or a(55) > m2 Then GoTo 550:
If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
a(54) = 0.25 * s1 - a(61): If a(54) < m1 Or a(54) > m2 Then GoTo 540:
If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
a(53) = 0.25 * s1 - a(62): If a(53) < m1 Or a(53) > m2 Then GoTo 530:
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(52) = -0.25 * s1 + a(60) + a(61) + a(62): If a(52) < m1 Or a(52) > m2 Then GoTo 520:
If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
a(51) = 0.25 * s1 - a(60): If a(51) < m1 Or a(51) > m2 Then GoTo 510:
If b(a(51)) = 0 Then b(a(51)) = a(51): c(51) = a(51) Else GoTo 510
a(50) = 0.25 * s1 + a(58) - a(61) - a(62): If a(50) < m1 Or a(50) > m2 Then GoTo 500:
If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
a(49) = 0.25 * s1 - a(58): If a(49) < m1 Or a(49) > m2 Then GoTo 490:
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
For j48 = m1 To m2 'a(48) = 13
If b(j48) = 0 Then b(j48) = j48: c(48) = j48 Else GoTo 480
a(48) = j48
a(47) = -0.25 * s1 + a(48) + a(56) + a(64): If a(47) < m1 Or a(47) > m2 Then GoTo 470:
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(46) = 0.25 * s1 - a(48) - a(56) + a(61): If a(46) < m1 Or a(46) > m2 Then GoTo 460:
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(45) = 0.5 * s1 - a(48) - a(61) - a(64): If a(45) < m1 Or a(45) > m2 Then GoTo 450:
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(44) = (-0.25 * s1 + 2 * a(48) + a(56) - 2 * a(60) + a(63) + 2 * a(64)) / 2:
j44 = Int(a(44)): If j44 <> a(44) Then GoTo 440
If a(44) < m1 Or a(44) > m2 Then GoTo 440:
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(43) = -0.5 * s1 + a(44) + 2 * a(60) + a(61) + a(62): If a(43) < m1 Or a(43) > m2 Then GoTo 430:
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(42) = -a(43) - a(58) + a(60) + a(61) + a(62): If a(42) < m1 Or a(42) > m2 Then GoTo 420:
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(41) = a(42) + 2 * a(58) - a(61) - a(62): If a(41) < m1 Or a(41) > m2 Then GoTo 410:
If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(40) = 0.5 * s1 - a(48) - a(56) - a(64): If a(40) < m1 Or a(40) > m2 Then GoTo 400:
If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(39) = 0.25 * s1 - a(48): If a(39) < m1 Or a(39) > m2 Then GoTo 390:
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(38) = -0.25 * s1 + a(48) + a(61) + a(64): If a(38) < m1 Or a(38) > m2 Then GoTo 380:
If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
a(37) = 0.5 * s1 - a(38) - a(39) - a(40): If a(37) < m1 Or a(37) > m2 Then GoTo 370:
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(36) = 0.25 * s1 + a(41) - a(58) - a(60): If a(36) < m1 Or a(36) > m2 Then GoTo 360:
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(35) = 0.5 * s1 - a(36) - a(37) - a(38): If a(35) < m1 Or a(35) > m2 Then GoTo 350:
If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(34) = -a(35) - a(58) + a(60) + a(61) + a(62): If a(34) < m1 Or a(34) > m2 Then GoTo 340:
If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(33) = 0.5 * s1 - a(34) - a(35) - a(36): If a(33) < m1 Or a(33) > m2 Then GoTo 330:
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
For j32 = m1 To m2 'a(32) = 51
If b(j32) = 0 Then b(j32) = j32: c(32) = j32 Else GoTo 320
a(32) = j32
a(31) = 0.25 * s1 + a(32) - a(56) - a(64): If a(31) < m1 Or a(31) > m2 Then GoTo 310:
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(30) = 0.25 * s1 - a(32) + a(56) - a(61): If a(30) < m1 Or a(30) > m2 Then GoTo 300:
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(29) = 0.5 * s1 - a(30) - a(31) - a(32): If a(29) < m1 Or a(29) > m2 Then GoTo 290:
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(28) = (-0.25 * s1 + 2 * a(32) - a(56) + 2 * a(60) + a(61) + a(62) - a(64)) / 2:
j28 = Int(a(28)): If j28 <> a(28) Then GoTo 280
If a(28) < m1 Or a(28) > m2 Then GoTo 280:
If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(27) = 0.5 * s1 - a(28) - a(29) - a(30): If a(27) < m1 Or a(27) > m2 Then GoTo 270:
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(26) = -a(28) + a(58) + a(60): If a(26) < m1 Or a(26) > m2 Then GoTo 260:
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(25) = 0.5 * s1 - a(26) - a(27) - a(28): If a(25) < m1 Or a(25) > m2 Then GoTo 250:
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(24) = -a(32) + a(56) + a(64): If a(24) < m1 Or a(24) > m2 Then GoTo 240:
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(23) = 0.25 * s1 - a(32): If a(23) < m1 Or a(23) > m2 Then GoTo 230:
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = a(30) + 2 * a(32) - a(56) - a(64): If a(22) < m1 Or a(22) > m2 Then GoTo 220:
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = 0.5 * s1 - a(22) - a(23) - a(24): If a(21) < m1 Or a(21) > m2 Then GoTo 210:
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = -0.25 * s1 + a(25) + a(58) + a(60): If a(20) < m1 Or a(20) > m2 Then GoTo 200:
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = 0.5 * s1 - a(20) - a(21) - a(22): If a(19) < m1 Or a(19) > m2 Then GoTo 190:
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(18) = -a(20) + a(58) + a(60): If a(18) < m1 Or a(18) > m2 Then GoTo 180:
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(17) = 0.5 * s1 - a(18) - a(19) - a(20): If a(17) < m1 Or a(17) > m2 Then GoTo 170:
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
For j16 = m1 To m2 'a(16) = 9
If b(j16) = 0 Then b(j16) = j16: c(16) = j16 Else GoTo 160
a(16) = j16
a(15) = -0.25 * s1 + a(16) + a(56) + a(64): If a(15) < m1 Or a(15) > m2 Then GoTo 150:
a(14) = 0.25 * s1 - a(16) + a(21) - a(32): If a(14) < m1 Or a(14) > m2 Then GoTo 150:
a(13) = 0.5 * s1 - a(14) - a(15) - a(16): If a(13) < m1 Or a(13) > m2 Then GoTo 150:
a(12) = 0.25 * s1 + a(16) - a(17) + a(32) - a(58) - a(60):
If a(12) < m1 Or a(12) > m2 Then GoTo 150:
a(11) = 0.5 * s1 - a(12) - a(13) - a(14): If a(11) < m1 Or a(11) > m2 Then GoTo 150:
a(10) = -a(11) - a(58) + a(60) + a(61) + a(62):
If a(10) < m1 Or a(10) > m2 Then GoTo 150:
a(9) = 0.5 * s1 - a(10) - a(11) - a(12): If a(9) < m1 Or a(9) > m2 Then GoTo 150:
a(8) = 0.5 * s1 - a(16) - a(24) - a(32): If a(8) < m1 Or a(8) > m2 Then GoTo 150:
a(7) = 0.5 * s1 - a(16) - a(21) - a(30): If a(7) < m1 Or a(7) > m2 Then GoTo 150:
a(6) = 0.5 * s1 - a(13) - a(24) - a(31): If a(6) < m1 Or a(6) > m2 Then GoTo 150:
a(5) = 0.5 * s1 - a(6) - a(7) - a(8): If a(5) < m1 Or a(5) > m2 Then GoTo 150:
a(4) = 0.5 * s1 - a(12) - a(20) - a(28): If a(4) < m1 Or a(4) > m2 Then GoTo 150:
a(3) = 0.5 * s1 - a(4) - a(5) - a(6): If a(3) < m1 Or a(3) > m2 Then GoTo 150:
a(2) = 0.5 * s1 - a(9) - a(20) - a(27): If a(2) < m1 Or a(2) > m2 Then GoTo 150:
a(1) = 0.5 * s1 - a(2) - a(3) - a(4): If a(1) < m1 Or a(1) > m2 Then GoTo 150:
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 150
n9 = n9 + 1
GoSub 650 'Print results (squares)
' GoSub 645 'Print results (selected numbers)
150 b(c(16)) = 0: c(16) = 0
160 Next j16
b(c(17)) = 0: c(17) = 0
170 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(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 b(c(24)) = 0: c(24) = 0
240 b(c(25)) = 0: c(25) = 0
250 b(c(26)) = 0: c(26) = 0
260 b(c(27)) = 0: c(27) = 0
270 b(c(28)) = 0: c(28) = 0
280 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 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 b(c(34)) = 0: c(34) = 0
340 b(c(35)) = 0: c(35) = 0
350 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 b(c(38)) = 0: c(38) = 0
380 b(c(39)) = 0: c(39) = 0
390 b(c(40)) = 0: c(40) = 0
400 b(c(41)) = 0: c(41) = 0
410 b(c(42)) = 0: c(42) = 0
420 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 b(c(45)) = 0: c(45) = 0
450 b(c(46)) = 0: c(46) = 0
460 b(c(47)) = 0: c(47) = 0
470 b(c(48)) = 0: c(48) = 0
480 Next j48
b(c(49)) = 0: c(49) = 0
490 b(c(50)) = 0: c(50) = 0
500 b(c(51)) = 0: c(51) = 0
510 b(c(52)) = 0: c(52) = 0
520 b(c(53)) = 0: c(53) = 0
530 b(c(54)) = 0: c(54) = 0
540 b(c(55)) = 0: c(55) = 0
550 b(c(56)) = 0: c(56) = 0
560 b(c(57)) = 0: c(57) = 0
570 b(c(58)) = 0: c(58) = 0
580 Next j58
b(c(59)) = 0: c(59) = 0
590 b(c(60)) = 0: c(60) = 0
600 Next j60
b(c(61)) = 0: c(61) = 0
610 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(63)) = 0: c(63) = 0
630 Next j63
b(c(64)) = 0: c(64) = 0
640 Next j64
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqr8d2")
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
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
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 64
a2 = a(j1)
For j2 = (1 + j1) To 64
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
End Sub
