' Generates Four Way V-ZigZag Ultra Magic Squares of order 8
' Tested with Office 2007 under Windows 7
Sub ZigZag8()
Dim a1(64), a(64), b1(64), b(64), c(64)
y = MsgBox("Locked", vbCritical, "Routine ZigZag8")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 2
Cells(k1, 1).Select: Cells(k1, 1).Value = j100
' Define variables
GoSub 2000 ' Read Natural Numbers (j100 = 1 To 1)
m64 = Sheets("Lines8").Cells(j100, 1).Value
m63 = Sheets("Lines8").Cells(j100, 2).Value
m62 = Sheets("Lines8").Cells(j100, 3).Value
m61 = Sheets("Lines8").Cells(j100, 4).Value
m60 = Sheets("Lines8").Cells(j100, 5).Value
m59 = Sheets("Lines8").Cells(j100, 6).Value
For j64 = m64 To m64 ''m1 To m2 / 2 '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) = s1 / 4 - a(64): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j63 = m63 To m63 ''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(2) = s1 / 4 - a(63): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j62 = m62 To m62 ''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(3) = s1 / 4 - a(62): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j61 = m61 To m61 ''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(4) = s1 / 4 - a(61): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j60 = m60 To m60 ''m1 To m2 'a(60)
If b(a1(j60)) = 0 Then b(a1(j60)) = a1(j60): c(60) = a1(j60) Else GoTo 600
a(60) = a1(j60)
a(58) = 0.5 * s1 - a(60) - a(62) - a(64)
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) = s1 / 4 - a(58): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(5) = s1 / 4 - a(60): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j59 = m59 To m59 ''m1 To m2 'a(59)
If b(a1(j59)) = 0 Then b(a1(j59)) = a1(j59): c(59) = a1(j59) Else GoTo 590
a(59) = a1(j59)
a(57) = 0.5 * s1 - a(59) - a(61) - a(63)
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) = s1 / 4 - a(57): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(6) = s1 / 4 - a(59): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
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(9) = s1 / 4 - a(56): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j55 = m1 To m2 'a(55)
If b(a1(j55)) = 0 Then b(a1(j55)) = a1(j55): c(55) = a1(j55) Else GoTo 550
a(55) = a1(j55)
a(48) = 0.5 * s1 - a(55) - a(62) - a(64)
If a(48) < a1(m1) Or a(48) > a1(m2) Then GoTo 480:
If b1(a(48)) = 0 Then GoTo 480:
If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
a(17) = s1 / 4 - a(48): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(10) = s1 / 4 - a(55): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
For j54 = m1 To m2 '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(45) = 0.5 * s1 - a(54) - a(61) - a(63)
If a(45) < a1(m1) Or a(45) > a1(m2) Then GoTo 450:
If b1(a(45)) = 0 Then GoTo 450:
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(43) = -0.5 * s1 + 2 * a(54) + a(56) - a(59) + a(61) + 2 * a(63)
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(38) = -0.5 * s1 + a(54) + a(56) + a(61) + 2 * a(63)
If a(38) < a1(m1) Or a(38) > a1(m2) Then GoTo 380:
If b1(a(38)) = 0 Then GoTo 380:
If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
a(34) = 0.5 * s1 - a(54) - a(56) + a(59) - a(61) - a(63)
If a(34) < a1(m1) Or a(34) > a1(m2) Then GoTo 340:
If b1(a(34)) = 0 Then GoTo 340:
If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(31) = s1 / 4 - a(34): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(27) = s1 / 4 - a(38): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(22) = s1 / 4 - a(43): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(20) = s1 / 4 - a(45): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(11) = s1 / 4 - a(54): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j53 = m1 To m2 'a(53)
If b(a1(j53)) = 0 Then b(a1(j53)) = a1(j53): c(53) = a1(j53) Else GoTo 530
a(53) = a1(j53)
a(42) = -s1 + a(53) + 2 * a(55) + a(60) + 3 * a(62) + 2 * a(64)
If a(42) < a1(m1) Or a(42) > a1(m2) Then GoTo 420:
If b1(a(42)) = 0 Then GoTo 420:
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(39) = -0.5 * s1 + a(53) + a(55) + 2 * a(62) + a(64)
If a(39) < a1(m1) Or a(39) > a1(m2) Then GoTo 390:
If b1(a(39)) = 0 Then GoTo 390:
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(35) = s1 - a(53) - a(55) - a(60) - 2 * a(62) - 2 * a(64)
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(30) = s1 / 4 - a(35): If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(26) = s1 / 4 - a(39): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(23) = s1 / 4 - a(42): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(12) = s1 / 4 - a(53): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j52 = m1 To m2 'a(52)
If b(a1(j52)) = 0 Then b(a1(j52)) = a1(j52): c(52) = a1(j52) Else GoTo 520
a(52) = a1(j52)
a(50) = 0.5 * s1 - a(52) - a(54) - a(56)
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(47) = s1 - a(52) - 2 * a(54) - 2 * a(56) + a(59) - a(61) - 2 * a(63)
If a(47) < a1(m1) Or a(47) > a1(m2) Then GoTo 470:
If b1(a(47)) = 0 Then GoTo 470:
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(41) = -0.5 * s1 + a(52) + a(54) + a(56) + a(61) + a(63)
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) = a(52) + a(54) - a(59)
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(36) = 0.5 * s1 - a(52) - a(54) - a(63)
If a(36) < a1(m1) Or a(36) > a1(m2) Then GoTo 360:
If b1(a(36)) = 0 Then GoTo 360:
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(29) = s1 / 4 - a(36): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(25) = s1 / 4 - a(40): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(24) = s1 / 4 - a(41): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(18) = s1 / 4 - a(47): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(15) = s1 / 4 - a(50): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
a(13) = s1 / 4 - a(52): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j51 = m1 To m2 '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(49) = 0.5 * s1 - a(51) - a(53) - a(55)
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(46) = s1 + a(51) - a(53) - a(55) - a(60) - 3 * a(62) - 2 * a(64)
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(44) = -a(51) + a(62) + a(64)
If a(44) < a1(m1) Or a(44) > a1(m2) Then GoTo 440:
If b1(a(44)) = 0 Then GoTo 440:
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(37) = -a(51) - a(53) + a(60) + a(62) + a(64)
If a(37) < a1(m1) Or a(37) > a1(m2) Then GoTo 370:
If b1(a(37)) = 0 Then GoTo 370:
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(33) = a(51) + a(53) - a(62)
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) = s1 / 4 - a(33): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(28) = s1 / 4 - a(37): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(21) = s1 / 4 - a(44): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(19) = s1 / 4 - a(46): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(16) = s1 / 4 - a(49): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(14) = s1 / 4 - a(51): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
' 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
5
b(c(14)) = 0: c(14) = 0
140 b(c(16)) = 0: c(16) = 0
160 b(c(19)) = 0: c(19) = 0
190 b(c(21)) = 0: c(21) = 0
210 b(c(28)) = 0: c(28) = 0
280 b(c(32)) = 0: c(32) = 0
320 b(c(33)) = 0: c(33) = 0
330 b(c(37)) = 0: c(37) = 0
370 b(c(44)) = 0: c(44) = 0
440 b(c(46)) = 0: c(46) = 0
460 b(c(49)) = 0: c(49) = 0
490 b(c(51)) = 0: c(51) = 0
510 Next j51
b(c(13)) = 0: c(13) = 0
130 b(c(15)) = 0: c(15) = 0
150 b(c(18)) = 0: c(18) = 0
180 b(c(24)) = 0: c(24) = 0
240 b(c(25)) = 0: c(25) = 0
250 b(c(29)) = 0: c(29) = 0
290 b(c(36)) = 0: c(36) = 0
360 b(c(40)) = 0: c(40) = 0
400 b(c(41)) = 0: c(41) = 0
410 b(c(47)) = 0: c(47) = 0
470 b(c(50)) = 0: c(50) = 0
500 b(c(52)) = 0: c(52) = 0
520 Next j52
b(c(12)) = 0: c(12) = 0
120 b(c(23)) = 0: c(23) = 0
230 b(c(26)) = 0: c(26) = 0
260 b(c(30)) = 0: c(30) = 0
300 b(c(35)) = 0: c(35) = 0
350 b(c(39)) = 0: c(39) = 0
390 b(c(42)) = 0: c(42) = 0
420 b(c(53)) = 0: c(53) = 0
530 Next j53
b(c(11)) = 0: c(11) = 0
110 b(c(20)) = 0: c(20) = 0
200 b(c(22)) = 0: c(22) = 0
220 b(c(27)) = 0: c(27) = 0
270 b(c(31)) = 0: c(31) = 0
310 b(c(34)) = 0: c(34) = 0
340 b(c(38)) = 0: c(38) = 0
380 b(c(43)) = 0: c(43) = 0
430 b(c(45)) = 0: c(45) = 0
450 b(c(54)) = 0: c(54) = 0
540 Next j54
b(c(10)) = 0: c(10) = 0
100 b(c(17)) = 0: c(17) = 0
170 b(c(48)) = 0: c(48) = 0
480 b(c(55)) = 0: c(55) = 0
550 Next j55
b(c(9)) = 0: c(9) = 0
90 b(c(56)) = 0: c(56) = 0
560 Next j56
b(c(6)) = 0: c(6) = 0
60 b(c(8)) = 0: c(8) = 0
80 b(c(57)) = 0: c(57) = 0
570 b(c(59)) = 0: c(59) = 0
590 Next j59
b(c(5)) = 0: c(5) = 0
50 b(c(7)) = 0: c(7) = 0
70 b(c(58)) = 0: c(58) = 0
580 b(c(60)) = 0: c(60) = 0
600 Next j60
b(c(4)) = 0: c(4) = 0
40 b(c(61)) = 0: c(61) = 0
610 Next j61
b(c(3)) = 0: c(3) = 0
30 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(2)) = 0: c(2) = 0
20 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
n10 = 0
Erase b, c:
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine ZigZag8")
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
' Sheets("Lines8").Cells(j100, 7).Value = "ok"
Return
' Read Natural Numbers
2000 m1 = 1: m2 = 64: s1 = 260
For i1 = 1 To 64
a1(i1) = i1
Next i1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
Return
End Sub
