' Constructs Composed Magic Squares of Order 11
' Tested with Office 2007 under Windows 7
Sub PriemE11()
Dim a1(121), a(64), a11(121), b1(121), b(121), c(64), Crnr3(2)
y = MsgBox("Locked", vbCritical, "Routine PriemE11")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
t1 = Timer
For j100 = 2 To 851
Cells(k1, 1).Select: Cells(k1, 1).Value = j100
GoSub 2010 'Redefine Integers
' Read Center Square (3 x 3)
For i1 = 1 To 9
a(i1) = Sheets("Lines3a").Cells(j100, i1).Value
Next i1
' Store in a11()
a11(49) = a(1): a11(50) = a(2): a11(51) = a(3):
a11(60) = a(4): a11(61) = a(5): a11(62) = a(6):
a11(71) = a(7): a11(72) = a(8): a11(73) = a(9):
n32 = 9: GoSub 900 'Remove used integers from available integers
' Complete Eccentrc Squares A1/2 (5 x 5)
Crnr3(1) = a11(51) 'Square 1
Crnr3(2) = a11(71) 'Square 2
i35 = 1
For n10 = 1 To 2
Erase a, b, c
GoSub 5000: If fl1 = 0 Then GoTo 1000
Select Case n10
Case 1:
a11(27) = a(1): a11(28) = a(6): a11(29) = a(9): a11(30) = a(10): a11(31) = a(11):
a11(38) = a(5): a11(39) = a(2): a11(40) = a(12): a11(41) = a(13): a11(42) = a(14):
a11(52) = a(16): a11(53) = a(15):
a11(63) = a(3): a11(64) = a(7):
a11(74) = a(8): a11(75) = a(4):
n32 = 16: GoSub 900 'Remove used integers from available integers
i35 = 2
Case 2:
a11(47) = a(4): a11(48) = a(8):
a11(58) = a(7): a11(59) = a(3):
a11(69) = a(15): a11(70) = a(16):
a11(80) = a(14): a11(81) = a(13): a11(82) = a(12): a11(83) = a(2): a11(84) = a(5):
a11(91) = a(11): a11(92) = a(10): a11(93) = a(9): a11(94) = a(6): a11(95) = a(1):
n32 = 16: GoSub 900 'Remove used integers from available integers
End Select
Next n10
' Complete Eccentrc Squares B1/2 (7 x 7)
Crnr3(1) = a11(29) + a11(41) + a11(53) ' Square 1
Crnr3(2) = a11(69) + a11(81) + a11(93) ' Square 2
i35 = 1
For n10 = 1 To 2
Erase a, b, c
GoSub 3000: If fl1 = 0 Then GoTo 1000
GoSub 7000: If fl1 = 0 Then GoTo 1000
Select Case n10
Case 1:
a11(5) = a(10): a11(6) = a(15): a11(7) = a(18): a11(8) = a(20): a11(9) = a(8): a11(10) = a(9): a11(11) = a(7):
a11(16) = a(14): a11(17) = a(11): a11(18) = a(19): a11(19) = a(21): a11(20) = a(2): a11(21) = a(3): a11(22) = a(1):
a11(32) = a(6): a11(33) = a(4):
a11(43) = a(25): a11(44) = a(24):
a11(54) = a(23): a11(55) = a(22):
a11(65) = a(12): a11(66) = a(16):
a11(76) = a(17): a11(77) = a(13):
n32 = 25: GoSub 900 'Remove used integers from available integers
i35 = 2
Case 2:
a11(45) = a(13): a11(46) = a(17):
a11(56) = a(16): a11(57) = a(12):
a11(67) = a(22): a11(68) = a(23):
a11(78) = a(24): a11(79) = a(25):
a11(89) = a(4): a11(90) = a(6):
a11(100) = a(1): a11(101) = a(3): a11(102) = a(2): a11(103) = a(21): a11(104) = a(19): a11(105) = a(11): a11(106) = a(14):
a11(111) = a(7): a11(112) = a(9): a11(113) = a(8): a11(114) = a(20): a11(115) = a(18): a11(116) = a(15): a11(117) = a(10):
n32 = 25: GoSub 900 'Remove used integers from available integers
End Select
Next n10
' Generate Pan Magic Squares Pm1/2 ( 4 x 4)
' Complete Composed Magic Square E (11 x 11)
For n10 = 1 To 2
Erase a, b, c
GoSub 4000: If fl1 = 0 Then GoTo 1000
Select Case n10
Case 1:
a11(1) = a(1): a11(2) = a(2): a11(3) = a(3): a11(4) = a(4):
a11(12) = a(5): a11(13) = a(6): a11(14) = a(7): a11(15) = a(8):
a11(23) = a(9): a11(24) = a(10): a11(25) = a(11): a11(26) = a(12):
a11(34) = a(13): a11(35) = a(14): a11(36) = a(15): a11(37) = a(16):
n32 = 16: GoSub 900 'Remove used integers from available integers
i35 = 2
Case 2:
a11(85) = a(1): a11(86) = a(2): a11(87) = a(3): a11(88) = a(4):
a11(96) = a(5): a11(97) = a(6): a11(98) = a(7): a11(99) = a(8):
a11(107) = a(9): a11(108) = a(10): a11(109) = a(11): a11(110) = a(12):
a11(118) = a(13): a11(119) = a(14): a11(120) = a(15): a11(121) = a(16):
End Select
Next n10
500
GoSub 850 'Double Check Identical Integers
If fl1 = 1 Then
n9 = n9 + 1: GoSub 1650 'Print results (squares)
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
End If
1000 Erase b1, b, c
Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine PriemE11")
End
' Determine Magic Square Order 3
3000 fl1 = 1
For j9 = m1 To m2 'a(9)
If b1(a1(j9)) = 0 Then GoTo 3090
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 3090
a(9) = a1(j9)
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 3080
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 3080
a(8) = a1(j8)
a(7) = s3 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 3070:
If b1(a(7)) = 0 Then GoTo 3070
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 3070
a(6) = 4 * s3 / 3 - a(8) - 2 * a(9):
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 3060:
If b1(a(6)) = 0 Then GoTo 3060
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 3060
a(5) = s3 / 3:
a(4) = -2 * s3 / 3 + a(8) + 2 * a(9):
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 3040:
If b1(a(4)) = 0 Then GoTo 3040
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 3040
a(3) = -s3 / 3 + a(8) + a(9):
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 3030:
If b1(a(3)) = 0 Then GoTo 3030
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 3030
a(2) = 2 * s3 / 3 - a(8):
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 3020:
If b1(a(2)) = 0 Then GoTo 3020
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 3020
a(1) = 2 * s3 / 3 - a(9):
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 3010:
If b1(a(1)) = 0 Then GoTo 3010
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 3010
Return
b(c(1)) = 0: c(1) = 0
3010 b(c(2)) = 0: c(2) = 0
3020 b(c(3)) = 0: c(2) = 0
3030 b(c(4)) = 0: c(4) = 0
3040 b(c(5)) = 0: c(5) = 0
3050 b(c(6)) = 0: c(6) = 0
3060 b(c(7)) = 0: c(7) = 0
3070 b(c(8)) = 0: c(8) = 0
3080 Next j8
b(c(9)) = 0: c(9) = 0
3090 Next j9
fl1 = 0
Return
' Complete Eccentrc Squares A1/2 (5 x 5)
5000 fl1 = 1
' Determine Main Diagonal and related pairs
For j1 = m1 To m2
If b1(a1(j1)) = 0 Then GoTo 10
If b(a1(j1)) = 0 Then b(a1(j1)) = a1(j1): c(1) = a1(j1) Else GoTo 10
a(1) = a1(j1)
a(5) = Pr3 - a(1): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j2 = m1 To m2
If b1(a1(j2)) = 0 Then GoTo 20
If b(a1(j2)) = 0 Then b(a1(j2)) = a1(j2): c(2) = a1(j2) Else GoTo 20
a(2) = a1(j2)
a(6) = Pr3 - a(2): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j3 = m1 To m2
If b1(a1(j3)) = 0 Then GoTo 30
If b(a1(j3)) = 0 Then b(a1(j3)) = a1(j3): c(3) = a1(j3) Else GoTo 30
a(3) = a1(j3)
a(7) = Pr3 - a(3): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(4) = (s5 - Crnr3(i35)) - a(3) - a(2) - a(1)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 40:
If b1(a(4)) = 0 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(8) = Pr3 - a(4): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
' Determine remainder of the pairs
For j9 = m1 To m2
If b1(a1(j9)) = 0 Then GoTo 90
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 90
a(9) = a1(j9)
a(12) = Pr3 - a(9): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j10 = m1 To m2
If b1(a1(j10)) = 0 Then GoTo 100
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(14) = Pr3 - a(10): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(11) = s5 - a(1) - a(6) - a(9) - a(10)
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(13) = Pr3 - a(11): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(15) = s5 - a(4) - a(7) - a(14) - a(11)
If a(15) < a1(m1) Or a(15) > a1(m2) Then GoTo 150:
If b1(a(15)) = 0 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
a(16) = Pr3 - a(15): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
If a(9) + a(13) + a(15) >= 179 Then Return 'Change parameter for more results (149 ... 194)
b(c(16)) = 0: c(16) = 0
160 b(c(15)) = 0: c(15) = 0
150 b(c(13)) = 0: c(13) = 0
130 b(c(11)) = 0: c(11) = 0
110 b(c(14)) = 0: c(14) = 0
140 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(12)) = 0: c(12) = 0
120 b(c(9)) = 0: c(9) = 0
90 Next j9
b(c(8)) = 0: c(8) = 0
80 b(c(4)) = 0: c(4) = 0
40 b(c(7)) = 0: c(7) = 0
70 b(c(3)) = 0: c(3) = 0
30 Next j3
b(c(6)) = 0: c(6) = 0
60 b(c(2)) = 0: c(2) = 0
20 Next j2
b(c(5)) = 0: c(5) = 0
50 b(c(1)) = 0: c(1) = 0
10 Next j1
fl1 = 0
Return
' Complete Eccentrc Squares B1/2 (7 x 7)
' Main Diagonal and Related Pairs
7000 fl1 = 1
For j10 = m1 To m2
If b1(a1(j10)) = 0 Then GoTo 7100
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 7100
a(10) = a1(j10)
a(14) = Pr3 - a(10): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 7140
For j11 = m1 To m2
If b1(a1(j11)) = 0 Then GoTo 7110
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 7110
a(11) = a1(j11)
a(15) = Pr3 - a(11): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 7150
For j12 = m1 To m2
If b1(a1(j12)) = 0 Then GoTo 7120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 7120
a(12) = a1(j12)
a(16) = Pr3 - a(12): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 7160
a(13) = (s7 - Crnr3(i35)) - a(12) - a(11) - a(10)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 7130:
If b1(a(13)) = 0 Then GoTo 7130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 7130
a(17) = Pr3 - a(13): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 7170
For j18 = m1 To m2
If b1(a1(j18)) = 0 Then GoTo 7180
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 7180
a(18) = a1(j18)
a(19) = Pr3 - a(18): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 7190
a(20) = s7 - s3 - a(10) - a(15) - a(18)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 7200:
If b1(a(20)) = 0 Then GoTo 7200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 7200
a(21) = Pr3 - a(20): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 7210
For j22 = m1 To m2
If b1(a1(j22)) = 0 Then GoTo 7220
If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 7220
a(22) = a1(j22)
a(23) = Pr3 - a(22): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 7230
a(24) = s7 - s3 - a(13) - a(16) - a(22)
If a(24) < a1(m1) Or a(24) > a1(m2) Then GoTo 7240:
If b1(a(24)) = 0 Then GoTo 7240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 7240
a(25) = Pr3 - a(24): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 7250
Return
b(c(25)) = 0: c(25) = 0
7250 b(c(24)) = 0: c(24) = 0
7240 b(c(23)) = 0: c(23) = 0
7230 b(c(22)) = 0: c(22) = 0
7220 Next j22
b(c(21)) = 0: c(21) = 0
7210 b(c(20)) = 0: c(20) = 0
7200 b(c(19)) = 0: c(19) = 0
7190 b(c(18)) = 0: c(18) = 0
7180 Next j18
b(c(17)) = 0: c(17) = 0
7170 b(c(13)) = 0: c(13) = 0
7130 b(c(16)) = 0: c(16) = 0
7160 b(c(12)) = 0: c(12) = 0
7120 Next j12
b(c(15)) = 0: c(15) = 0
7150 b(c(11)) = 0: c(11) = 0
7110 Next j11
b(c(14)) = 0: c(14) = 0
7140 b(c(10)) = 0: c(10) = 0
7100 Next j10
fl1 = 0
Return
' Generate Pan Magic Squares Pm1/2 (4 x 4)
4000 fl1 = 1
For j16 = m1 To m2 'a(16)
If b1(a1(j16)) = 0 Then GoTo 4160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 4160
a(16) = a1(j16)
For j15 = m1 To m2 'a(15)
If b1(a1(j15)) = 0 Then GoTo 4150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 4150
a(15) = a1(j15)
For j14 = m1 To m2 'a(14)
If b1(a1(j14)) = 0 Then GoTo 4140
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 4140
a(14) = a1(j14)
a(13) = s4 - a(14) - a(15) - a(16)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 4130
If b1(a(13)) = 0 Then GoTo 4130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 4130
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 4120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 4120
a(12) = a1(j12)
a(11) = s4 - a(12) - a(15) - a(16)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 4070
If b1(a(11)) = 0 Then GoTo 4070
a(10) = a(12) - a(14) + a(16)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 4070
If b1(a(10)) = 0 Then GoTo 4070
a(9) = -a(12) + a(14) + a(15)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 4070
If b1(a(9)) = 0 Then GoTo 4070
a(8) = 0.5 * s4 - a(14)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 4070
If b1(a(8)) = 0 Then GoTo 4070
a(7) = -0.5 * s4 + a(14) + a(15) + a(16)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 4070:
If b1(a(7)) = 0 Then GoTo 4070
a(6) = 0.5 * s4 - a(16)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 4070:
If b1(a(6)) = 0 Then GoTo 4070
a(5) = 0.5 * s4 - a(15)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 4070:
If b1(a(5)) = 0 Then GoTo 4070
a(4) = 0.5 * s4 - a(12) + a(14) - a(16)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 4070:
If b1(a(4)) = 0 Then GoTo 4070
a(3) = 0.5 * s4 + a(12) - a(14) - a(15)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 4070:
If b1(a(3)) = 0 Then GoTo 4070
a(2) = 0.5 * s4 - a(12)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 4070:
If b1(a(2)) = 0 Then GoTo 4070
a(1) = -0.5 * s4 + a(12) + a(15) + a(16)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 4070:
If b1(a(1)) = 0 Then GoTo 4070
' Exclude solutions with identical numbers (PM4)
n32 = 16: GoSub 800: If fl1 = 0 Then GoTo 4070
Return
4070 b(c(12)) = 0: c(12) = 0
4120 Next j12
b(c(13)) = 0: c(13) = 0
4130 b(c(14)) = 0: c(14) = 0
4140 Next j14
b(c(15)) = 0: c(15) = 0
4150 Next j15
b(c(16)) = 0: c(16) = 0
4160 Next j16
fl1 = 0
Return
' Check Identical Numbers a()
800 fl1 = 1
For i1 = 1 To n32
a20 = a(i1)
For i2 = (1 + i1) To n32
If a20 = a(i2) Then fl1 = 0: Return
Next i2
Next i1
Return
' Double Check Identical Numbers a11()
850 fl1 = 1
For i1 = 1 To 121
a20 = a11(i1): If a20 = 0 Then GoTo 860
For i2 = (1 + i1) To 121
If a20 = a11(i2) Then fl1 = 0: Return
Next i2
860 Next i1
Return
' Remove used pairs from b1()
900 For i1 = 1 To n32
b1(a(i1)) = 0
Next i1
Return
' Print results (lines)
1640 Cells(n9, 226).Select
For i1 = 1 To 225
Cells(n9, i1).Value = a11(i1)
Next i1
Cells(n9, 226).Value = s15
Cells(n9, 227).Value = j100
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 4 Then
n2 = 1: k1 = k1 + 12: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 12
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = j100
i3 = 0
For i1 = 1 To 11
For i2 = 1 To 11
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a11(i3)
Next i2
Next i1
Return
' Define integer
2010 Pr3 = 122: Cntr3 = 61: nVar = 121
s3 = 3 * Cntr3 'MC3
s4 = 4 * Cntr3 'MC4
s5 = 5 * Cntr3 'MC5
s7 = 7 * Cntr3 'MC7
s11 = 11 * Cntr3 'MC11
s15 = 15 * Cntr3 'MC15
Erase b1
For i1 = 1 To nVar
a1(i1) = i1: b1(i1) = i1
Next i1
m1 = 1: m2 = nVar
Return
End Sub
