' Generates Cocentric Pan Magic Squares of order 8, Magic Sum 260
' Sayles Properties
' Tested with Office 2007 under Windows 7
Sub MagSqrs827()
Dim a(64), b(64), c(64), a1(16, 4), m(2, 6), b1(4)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr827")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 64: s1 = 260
' Generate data
Sheets("Klad1").Select
t1 = Timer
' Define Ranges with Consecutive Integers
a1(1, 1) = 1
For j1 = 1 To 16
If j1 <> 1 Then a1(j1, 1) = a1(j1 - 1, 1) + 4
For j2 = 1 To 4
If j2 <> 1 Then a1(j1, j2) = a1(j1, j2 - 1) + 1
If a1(j1, j2) > 64 Then a1(j1, j2) = a1(j1, j2) - 64
Next j2
Next j1
For j100 = 1 To 16 ''7
For j200 = 1 To 16 ''2
If j100 = j200 Then GoTo 2000
For j300 = 1 To 16 ''13
If j300 = j100 Or j300 = j200 Then GoTo 3000
For j400 = 1 To 16 ''3
If j400 = j100 Or j400 = j200 Or j400 = j300 Then GoTo 4000
For j500 = 1 To 16 ''14
If j500 = j100 Or j500 = j200 Or j500 = j300 Or j500 = j400 Then GoTo 5000
m(1, 1) = a1(j100, 1): m(2, 1) = a1(j100, 4) 'Consecutive Range 1
m(1, 2) = a1(j200, 1): m(2, 2) = a1(j200, 4) 'Consecutive Range 2
m(1, 3) = a1(j300, 1): m(2, 3) = a1(j300, 4) 'Consecutive Range 3
m(1, 4) = a1(j400, 1): m(2, 4) = a1(j400, 4) 'Consecutive Range 4
m(1, 5) = a1(j500, 1): m(2, 5) = a1(j500, 4) 'Consecutive Range 5
For j64 = m(1, 2) To m(2, 2) 'a(64) = 5
If b(j64) = 0 Then b(j64) = j64: c(64) = j64 Else GoTo 640
a(64) = j64
a(10) = 0.25 * s1 - a(64)
If a(10) < m1 Or a(10) > m2 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
For j63 = m(1, 3) To m(2, 3) 'a(63) = 52
If b(j63) = 0 Then b(j63) = j63: c(63) = j63 Else GoTo 630
a(63) = j63
a(9) = 0.25 * s1 - a(63)
If a(9) < m1 Or a(9) > m2 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j62 = m(1, 4) To m(2, 4) 'a(62) = 11
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
a(12) = 0.25 * s1 - a(62)
If a(12) < m1 Or a(12) > m2 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(11) = -0.25 * s1 + a(62) + a(63) + a(64)
If a(11) < m1 Or a(11) > m2 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j60 = m(1, 2) To m(2, 2) 'a(60) = 7
If b(j60) = 0 Then b(j60) = j60: c(60) = j60 Else GoTo 600
a(60) = j60
a(59) = -a(60) + a(63) + a(64)
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
a(58) = -a(60) + a(62) + a(64)
If a(58) < m1 Or a(58) > m2 Then GoTo 580:
If b(a(58)) = 0 Then b(a(58)) = a(58): c(58) = a(58) Else GoTo 580
a(57) = 0.5 * s1 + a(60) - a(62) - a(63) - 2 * a(64)
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(16) = 0.25 * s1 + a(60) - a(62) - a(64)
If a(16) < m1 Or a(16) > m2 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(15) = -0.25 * s1 - a(60) + a(62) + a(63) + 2 * a(64)
If a(15) < m1 Or a(15) > m2 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
a(14) = 0.25 * s1 - a(60)
If a(14) < m1 Or a(14) > m2 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = 0.25 * s1 + a(60) - a(63) - a(64)
If a(13) < m1 Or a(13) > m2 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j56 = m(1, 1) To m(2, 1) 'a(56) = 25
If b(j56) = 0 Then b(j56) = j56: c(56) = j56 Else GoTo 560
a(56) = j56
a(55) = 0.5 * s1 - a(56) - a(63) - 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) = a(56) + 2 * a(60) - a(62) - a(64)
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) = -a(56) - 2 * a(60) + a(62) + a(63) + 2 * a(64)
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) = a(56) + a(60) - a(64)
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) = 0.5 * s1 - a(56) - a(60) - a(63)
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) = a(56) + a(60) - 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) = -a(56) - a(60) + a(62) + a(63) + a(64)
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
a(8) = 0.25 * s1 - a(56) - a(60) + a(62)
If a(8) < m1 Or a(8) > m2 Then GoTo 80:
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(7) = 0.25 * s1 + a(56) + a(60) - a(62) - a(63) - a(64)
If a(7) < m1 Or a(7) > m2 Then GoTo 70:
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = 0.25 * s1 - a(56) - a(60) + a(64)
If a(6) < m1 Or a(6) > m2 Then GoTo 60:
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = -0.25 * s1 + a(56) + a(60) + a(63)
If a(5) < m1 Or a(5) > m2 Then GoTo 50:
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(4) = 0.25 * s1 - a(56) - 2 * a(60) + a(62) + a(64)
If a(4) < m1 Or a(4) > m2 Then GoTo 40:
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(3) = 0.25 * s1 + a(56) + 2 * a(60) - a(62) - a(63) - 2 * a(64)
If a(3) < m1 Or a(3) > m2 Then GoTo 30:
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = 0.25 * s1 - a(56)
If a(2) < m1 Or a(2) > m2 Then GoTo 20:
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = -0.25 * s1 + a(56) + a(63) + a(64)
If a(1) < m1 Or a(1) > m2 Then GoTo 10:
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j48 = m(1, 5) To m(2, 5) 'a(48) = 55
If b(j48) = 0 Then b(j48) = j48: c(48) = j48 Else GoTo 480
a(48) = j48
a(47) = -a(48) + a(63) + a(64):
If a(47) < m1 Or a(47) > m2 Then GoTo 470
a(46) = a(48) - 2 * a(60) + a(62) + a(64):
If a(46) < m1 Or a(46) > m2 Then GoTo 470
a(45) = 0.5 * s1 - a(48) + 2 * a(60) - a(62) - a(63) - 2 * a(64):
If a(45) < m1 Or a(45) > m2 Then GoTo 470
a(44) = a(48) - a(60) + a(64):
If a(44) < m1 Or a(44) > m2 Then GoTo 470
a(43) = -a(48) + a(60) + a(63):
If a(43) < m1 Or a(43) > m2 Then GoTo 470
a(42) = a(48) - a(60) + a(62):
If a(42) < m1 Or a(42) > m2 Then GoTo 470
a(41) = 0.5 * s1 - a(48) + a(60) - a(62) - a(63) - a(64):
If a(41) < m1 Or a(41) > m2 Then GoTo 470
a(40) = a(48) - a(56) - 2 * a(60) + 2 * a(62) + a(64):
If a(40) < m1 Or a(40) > m2 Then GoTo 470
a(39) = 0.5 * s1 - a(48) + a(56) + 2 * a(60) - 2 * a(62) - a(63) - 2 * a(64):
If a(39) < m1 Or a(39) > m2 Then GoTo 470
a(38) = a(48) - a(56) - 2 * a(60) + a(62) + 2 * a(64):
If a(38) < m1 Or a(38) > m2 Then GoTo 470
a(37) = -a(48) + a(56) + 2 * a(60) - a(62) + a(63) - a(64):
If a(37) < m1 Or a(37) > m2 Then GoTo 470
a(36) = a(48) - a(56) - 3 * a(60) + 2 * a(62) + 2 * a(64):
If a(36) < m1 Or a(36) > m2 Then GoTo 470
a(35) = 0.5 * s1 - a(48) + a(56) + 3 * a(60) - 2 * a(62) - a(63) - 3 * a(64):
If a(35) < m1 Or a(35) > m2 Then GoTo 470
a(34) = a(48) - a(56) - a(60) + a(62) + a(64):
If a(34) < m1 Or a(34) > m2 Then GoTo 470
a(33) = -a(48) + a(56) + a(60) - a(62) + a(63):
If a(33) < m1 Or a(33) > m2 Then GoTo 470
a(32) = 0.25 * s1 - a(48) + a(60) - a(62):
If a(32) < m1 Or a(32) > m2 Then GoTo 470
a(31) = -0.25 * s1 + a(48) - a(60) + a(62) + a(63) + a(64):
If a(31) < m1 Or a(31) > m2 Then GoTo 470
a(30) = 0.25 * s1 - a(48) + a(60) - a(64):
If a(30) < m1 Or a(30) > m2 Then GoTo 470
a(29) = 0.25 * s1 + a(48) - a(60) - a(63):
If a(29) < m1 Or a(29) > m2 Then GoTo 470
a(28) = 0.25 * s1 - a(48) + 2 * a(60) - a(62) - a(64):
If a(28) < m1 Or a(28) > m2 Then GoTo 470
a(27) = -0.25 * s1 + a(48) - 2 * a(60) + a(62) + a(63) + 2 * a(64):
If a(27) < m1 Or a(27) > m2 Then GoTo 470
a(26) = 0.25 * s1 - a(48):
If a(26) < m1 Or a(26) > m2 Then GoTo 470
a(25) = 0.25 * s1 + a(48) - a(63) - a(64):
If a(25) < m1 Or a(25) > m2 Then GoTo 470
a(24) = 0.25 * s1 - a(48) + a(56) + a(60) - a(62) - a(64):
If a(24) < m1 Or a(24) > m2 Then GoTo 470
a(23) = 0.25 * s1 + a(48) - a(56) - a(60) + a(62) - a(63):
If a(23) < m1 Or a(23) > m2 Then GoTo 470
a(22) = 0.25 * s1 - a(48) + a(56) + 3 * a(60) - 2 * a(62) - 2 * a(64):
If a(22) < m1 Or a(22) > m2 Then GoTo 470
a(21) = -0.25 * s1 + a(48) - a(56) - 3 * a(60) + 2 * a(62) + a(63) + 3 * a(64):
If a(21) < m1 Or a(21) > m2 Then GoTo 470
a(20) = 0.25 * s1 - a(48) + a(56) + 2 * a(60) - a(62) - 2 * a(64):
If a(20) < m1 Or a(20) > m2 Then GoTo 470
a(19) = 0.25 * s1 + a(48) - a(56) - 2 * a(60) + a(62) - a(63) + a(64):
If a(19) < m1 Or a(19) > m2 Then GoTo 470
a(18) = 0.25 * s1 - a(48) + a(56) + 2 * a(60) - 2 * a(62) - a(64):
If a(18) < m1 Or a(18) > m2 Then GoTo 470
a(17) = -0.25 * s1 + a(48) - a(56) - 2 * a(60) + 2 * a(62) + a(63) + 2 * a(64):
If a(17) < m1 Or a(17) > m2 Then GoTo 470
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 15
' Double Check Consecutive Integers
GoSub 900: If fl1 = 0 Then GoTo 15
n9 = n9 + 1
GoSub 650 'Print results (squares)
' GoSub 645 'Print results (selected numbers)
Erase b, c: GoTo 5000 'Print only first square (Option)
15
470 b(c(48)) = 0: c(48) = 0
480 Next j48
b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 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 Next j56
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
150 b(c(16)) = 0: c(16) = 0
160 b(c(57)) = 0: c(57) = 0
570 b(c(58)) = 0: c(58) = 0
580 b(c(59)) = 0: c(59) = 0
590 b(c(60)) = 0: c(60) = 0
600 Next j60
b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 b(c(61)) = 0: c(61) = 0
610 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(9)) = 0: c(9) = 0
90 b(c(63)) = 0: c(63) = 0
630 Next j63
b(c(10)) = 0: c(10) = 0
100 b(c(64)) = 0: c(64) = 0
640 Next j64
5000 Next j500
4000 Next j400
3000 Next j300
2000 Next j200
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqr827")
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
Range(Cells(k1, k2 + 1), Cells(k1, k2 + 6)).Font.Color = -4165632
' Cells(k1, k2 + 1).Value = n9 'Option (Fixed Ranges)
Cells(k1, k2 + 1).Value = j100
Cells(k1, k2 + 2).Value = j200
Cells(k1, k2 + 3).Value = j300
Cells(k1, k2 + 4).Value = j400
Cells(k1, k2 + 5).Value = j500
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): If a2 = 0 Then GoTo 805
For j2 = (1 + j1) To 64
If a2 = a(j2) Then fl1 = 0: Return
Next j2
805 Next j1
Return
' Double Check Consecutive Integers
900 fl1 = 1
b1(1) = a(1): b1(2) = a(5): b1(3) = a(33): b1(4) = a(37): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(2): b1(2) = a(6): b1(3) = a(34): b1(4) = a(38): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(3): b1(2) = a(7): b1(3) = a(35): b1(4) = a(39): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(4): b1(2) = a(8): b1(3) = a(36): b1(4) = a(40): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(9): b1(2) = a(13): b1(3) = a(41): b1(4) = a(45): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(10): b1(2) = a(14): b1(3) = a(42): b1(4) = a(46): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(11): b1(2) = a(15): b1(3) = a(43): b1(4) = a(47): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(12): b1(2) = a(16): b1(3) = a(44): b1(4) = a(48): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(17): b1(2) = a(21): b1(3) = a(49): b1(4) = a(53): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(18): b1(2) = a(22): b1(3) = a(50): b1(4) = a(54): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(19): b1(2) = a(23): b1(3) = a(51): b1(4) = a(55): GoSub 950: If fl1 = 0 Then Return
b1(1) = a(25): b1(2) = a(29): b1(3) = a(57): b1(4) = a(61): GoSub 950: If fl1 = 0 Then Return
Return
' Sorteren
950 k3 = 4: fl = 1
While fl
fl = 0
For j1 = 1 To k3 - 1
If b1(j1) > b1(j1 + 1) Then
b2 = b1(j1): b1(j1) = b1(j1 + 1): b1(j1 + 1) = b2
fl = 1: GoTo 5
End If
5 Next j1
k3 = k3 - 1
Wend
' Check Consecutive Integers
For j1 = 2 To 4
If b1(j1) - b1(j1 - 1) <> 1 Then fl1 = 0: Exit For
Next j1
Return
End Sub
