' Constructs 11 x 11 Associated Magic Squares based on:
' - One Magic Center Square (3 x 3), four Anti Symmetric Magic Corner Squares (4 x 4),
' - Four Anti Symmetric Magic Border Rectagles (3 x 4)
' Tested with Office 2007 under Windows 7
Sub Priem11f()
Dim a1(121), a(64), a11(121), b1(121), b(121), c(9), a2(121), b2(121), c2(121)
y = MsgBox("Locked", vbCritical, "Routine Priem11f")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm2 = "Cubes4" 'Simple Associated Magic Cubes
t1 = Timer
For j100 = 3 To 116
GoSub 2010 'Redefine Integers
' Read Semi Magic Corner Squares 4 x 4 (Simple Associated Magic Cubes)
For i1 = 1 To 64
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n32 = 64: GoSub 900 'Remove used integers from available integers
' Store Semi Magic Corner Squares in a11()
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):
a11(8) = a(17): a11(9) = a(18): a11(10) = a(19): a11(11) = a(20):
a11(19) = a(21): a11(20) = a(22): a11(21) = a(23): a11(22) = a(24):
a11(30) = a(25): a11(31) = a(26): a11(32) = a(27): a11(33) = a(28):
a11(41) = a(29): a11(42) = a(30): a11(43) = a(31): a11(44) = a(32):
a11(78) = a(33): a11(79) = a(34): a11(80) = a(35): a11(81) = a(36):
a11(89) = a(37): a11(90) = a(38): a11(91) = a(39): a11(92) = a(40):
a11(100) = a(41): a11(101) = a(42): a11(102) = a(43): a11(103) = a(44):
a11(111) = a(45): a11(112) = a(46): a11(113) = a(47): a11(114) = a(48):
a11(85) = a(49): a11(86) = a(50): a11(87) = a(51): a11(88) = a(52):
a11(96) = a(53): a11(97) = a(54): a11(98) = a(55): a11(99) = a(56):
a11(107) = a(57): a11(108) = a(58): a11(109) = a(59): a11(110) = a(60):
a11(118) = a(61): a11(119) = a(62): a11(120) = a(63): a11(121) = a(64):
Erase a
' Restore available pairs in a1()
n10 = 0
For j1 = 1 To pMax
If b1(j1) <> 0 Then
n10 = n10 + 1
a1(n10) = b1(j1)
End If
Next j1
m1 = 1: m2 = n10: n10 = 0
GoSub 2000 'Magic Square (3 x 3)
If fl1 = 0 Then GoTo 1000
GoSub 3000 'Magic rectangles (3 x 4)
If fl1 = 0 Then GoTo 1000
GoSub 850 'Double Check Identical Integers a11()
If fl1 = 1 Then
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
n9 = n9 + 1: GoSub 1650 'Print results (squares)
End If
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem11f")
End
' Determine Magic Square (3 x 3)
2000 fl1 = 1
For j9 = m1 To m2 'a(9)
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 160
a(9) = a1(j9)
For j8 = m1 To m2 'a(8)
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 120
a(8) = a1(j8)
a(7) = s3 - a(8) - a(9):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 110:
If b1(a(7)) = 0 Then GoTo 110
a(6) = 4 * s3 / 3 - a(8) - 2 * a(9):
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 110:
If b1(a(6)) = 0 Then GoTo 110
a(5) = s3 / 3:
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 110:
If b1(a(5)) = 0 Then GoTo 110
a(4) = -2 * s3 / 3 + a(8) + 2 * a(9):
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 110:
If b1(a(4)) = 0 Then GoTo 110
a(3) = -s3 / 3 + a(8) + a(9):
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 110:
If b1(a(3)) = 0 Then GoTo 110
a(2) = 2 * s3 / 3 - a(8):
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 110:
If b1(a(2)) = 0 Then GoTo 110
a(1) = 2 * s3 / 3 - a(9):
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 110:
If b1(a(1)) = 0 Then GoTo 110
' Exclude solutions with identical numbers a()
GoSub 800: If fl1 = 0 Then GoTo 110
GoSub 700 'Assign Center Square
n32 = 9: GoSub 900 'Remove used integers a() from available integers b1()
Return
110 b(c(8)) = 0: c(8) = 0
120 Next j8
b(c(9)) = 0: c(9) = 0
160 Next j9
fl1 = 0
Return
' Determine Anti Magic Rectangle (3 x 4)
3000 fl1 = 1
For jj12 = m1 To m2 'a2(12)
If b1(a1(jj12)) = 0 Then GoTo 125
If b2(a1(jj12)) = 0 Then b2(a1(jj12)) = a1(jj12): c2(12) = a1(jj12) Else GoTo 125
a2(12) = a1(jj12)
a2(13) = Pr3 - a2(12): If b2(a2(13)) = 0 Then b2(a2(13)) = a2(13): c2(13) = a2(13) Else GoTo 130
For jj11 = m1 To m2 'a2(11)
If b1(a1(jj11)) = 0 Then GoTo 115
If b2(a1(jj11)) = 0 Then b2(a1(jj11)) = a1(jj11): c2(11) = a1(jj11) Else GoTo 115
a2(11) = a1(jj11)
a2(14) = Pr3 - a2(11): If b2(a2(14)) = 0 Then b2(a2(14)) = a2(14): c2(14) = a2(14) Else GoTo 140
For jj10 = m1 To m2 'a2(10)
If b1(a1(jj10)) = 0 Then GoTo 100
If b2(a1(jj10)) = 0 Then b2(a1(jj10)) = a1(jj10): c2(10) = a1(jj10) Else GoTo 100
a2(10) = a1(jj10)
a2(15) = Pr3 - a2(10): If b2(a2(15)) = 0 Then b2(a2(15)) = a2(15): c2(15) = a2(15) Else GoTo 150
a2(9) = s4 - a2(10) - a2(11) - a2(12)
If a2(9) < a1(m1) Or a2(9) > a1(m2) Then GoTo 90
If b1(a2(9)) = 0 Then GoTo 90
If b2(a2(9)) = 0 Then b2(a2(9)) = a2(9): c2(9) = a2(9) Else GoTo 90
a2(16) = Pr3 - a2(9): If b2(a2(16)) = 0 Then b2(a2(16)) = a2(16): c2(16) = a2(16) Else GoTo 165
For jj8 = m1 To m2 'a2(8)
If b1(a1(jj8)) = 0 Then GoTo 80
If b2(a1(jj8)) = 0 Then b2(a1(jj8)) = a1(jj8): c2(8) = a1(jj8) Else GoTo 80
a2(8) = a1(jj8)
a2(17) = Pr3 - a2(8): If b2(a2(17)) = 0 Then b2(a2(17)) = a2(17): c2(17) = a2(17) Else GoTo 170
a2(4) = s3 - a2(8) - a2(12)
If a2(4) < a1(m1) Or a2(4) > a1(m2) Then GoTo 40
If b1(a2(4)) = 0 Then GoTo 40
If b2(a2(4)) = 0 Then b2(a2(4)) = a2(4): c2(4) = a2(4) Else GoTo 40
a2(21) = Pr3 - a2(4): If b2(a2(21)) = 0 Then b2(a2(21)) = a2(21): c2(21) = a2(21) Else GoTo 210
For jj7 = m1 To m2 'a2(7)
If b1(a1(jj7)) = 0 Then GoTo 70
If b2(a1(jj7)) = 0 Then b2(a1(jj7)) = a1(jj7): c2(7) = a1(jj7) Else GoTo 70
a2(7) = a1(jj7)
a2(18) = Pr3 - a2(7): If b2(a2(18)) = 0 Then b2(a2(18)) = a2(18): c2(18) = a2(18) Else GoTo 180
a2(3) = s3 - a2(7) - a2(11)
If a2(3) < a1(m1) Or a2(3) > a1(m2) Then GoTo 30
If b1(a2(3)) = 0 Then GoTo 30
If b2(a2(3)) = 0 Then b2(a2(3)) = a2(3): c2(3) = a2(3) Else GoTo 30
a2(22) = Pr3 - a2(3): If b2(a2(22)) = 0 Then b2(a2(22)) = a2(22): c2(22) = a2(22) Else GoTo 220
For jj6 = m1 To m2 'a2(6)
If b1(a1(jj6)) = 0 Then GoTo 60
If b2(a1(jj6)) = 0 Then b2(a1(jj6)) = a1(jj6): c2(6) = a1(jj6) Else GoTo 60
a2(6) = a1(jj6)
a2(19) = Pr3 - a2(6): If b2(a2(19)) = 0 Then b2(a2(19)) = a2(19): c2(19) = a2(19) Else GoTo 190
a2(2) = s3 - a2(6) - a2(10)
If a2(2) < a1(m1) Or a2(2) > a1(m2) Then GoTo 20
If b1(a2(2)) = 0 Then GoTo 20
If b2(a2(2)) = 0 Then b2(a2(2)) = a2(2): c2(2) = a2(2) Else GoTo 20
a2(23) = Pr3 - a2(2): If b2(a2(23)) = 0 Then b2(a2(23)) = a2(23): c2(23) = a2(23) Else GoTo 230
a2(5) = s4 - a2(6) - a2(7) - a2(8)
If a2(5) < a1(m1) Or a2(5) > a1(m2) Then GoTo 50
If b1(a2(5)) = 0 Then GoTo 50
If b2(a2(5)) = 0 Then b2(a2(5)) = a2(5): c2(5) = a2(5) Else GoTo 50
a2(20) = Pr3 - a2(5): If b2(a2(20)) = 0 Then b2(a2(20)) = a2(20): c2(20) = a2(20) Else GoTo 200
a2(1) = s3 - a2(5) - a2(9)
If a2(1) < a1(m1) Or a2(1) > a1(m2) Then GoTo 10
If b1(a2(1)) = 0 Then GoTo 10
If b2(a2(1)) = 0 Then b2(a2(1)) = a2(1): c2(1) = a2(1) Else GoTo 10
a2(24) = Pr3 - a2(1): If b2(a2(24)) = 0 Then b2(a2(24)) = a2(24): c2(24) = a2(24) Else GoTo 240
n10 = n10 + 1
Select Case n10
Case 1:
a11(5) = a2(9): a11(6) = a2(5): a11(7) = a2(1):
a11(16) = a2(10): a11(17) = a2(6): a11(18) = a2(2):
a11(27) = a2(11): a11(28) = a2(7): a11(29) = a2(3):
a11(38) = a2(12): a11(39) = a2(8): a11(40) = a2(4):
a11(82) = a2(21): a11(83) = a2(17): a11(84) = a2(13):
a11(93) = a2(22): a11(94) = a2(18): a11(95) = a2(14):
a11(104) = a2(23): a11(105) = a2(19): a11(106) = a2(15):
a11(115) = a2(24): a11(116) = a2(20): a11(117) = a2(16):
n32 = 12: GoSub 910 'Remove used pairs from b1()
Erase b2, c2: GoTo 125
Case 2:
a11(45) = a2(1): a11(46) = a2(2): a11(47) = a2(3): a11(48) = a2(4):
a11(56) = a2(5): a11(57) = a2(6): a11(58) = a2(7): a11(59) = a2(8):
a11(67) = a2(9): a11(68) = a2(10): a11(69) = a2(11): a11(70) = a2(12):
a11(52) = a2(13): a11(53) = a2(14): a11(54) = a2(15): a11(55) = a2(16):
a11(63) = a2(17): a11(64) = a2(18): a11(65) = a2(19): a11(66) = a2(20):
a11(74) = a2(21): a11(75) = a2(22): a11(76) = a2(23): a11(77) = a2(24):
Erase b2, c2: Return
End Select
5 b2(c2(24)) = 0: c2(24) = 0
240 b2(c2(1)) = 0: c2(2) = 0
10 b2(c2(20)) = 0: c2(20) = 0
200 b2(c2(5)) = 0: c2(5) = 0
50 b2(c2(23)) = 0: c2(23) = 0
230 b2(c2(2)) = 0: c2(2) = 0
20 b2(c2(19)) = 0: c2(19) = 0
190 b2(c2(6)) = 0: c2(6) = 0
60 Next jj6
b2(c2(22)) = 0: c2(22) = 0
220 b2(c2(3)) = 0: c2(3) = 0
30 b2(c2(18)) = 0: c2(18) = 0
180 b2(c2(7)) = 0: c2(7) = 0
70 Next jj7
b2(c2(21)) = 0: c2(21) = 0
210 b2(c2(4)) = 0: c2(4) = 0
40 b2(c2(17)) = 0: c2(17) = 0
170 b2(c2(8)) = 0: c2(8) = 0
80 Next jj8
b2(c2(16)) = 0: c2(16) = 0
165 b2(c2(9)) = 0: c2(9) = 0
90 b2(c2(15)) = 0: c2(15) = 0
150 b2(c2(10)) = 0: c2(10) = 0
100 Next jj10
b2(c2(14)) = 0: c2(14) = 0
140 b2(c2(11)) = 0: c2(11) = 0
115 Next jj11
b2(c2(13)) = 0: c2(13) = 0
130 b2(c2(12)) = 0: c2(12) = 0
125 Next jj12
fl1 = 0
Return
' Assign Center Square
700 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):
Return
' Double Check Identical Numbers a()
800 fl1 = 1
For i1 = 1 To 9
a20 = a(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 9
If a20 = a(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Exclude solutions with identical numbers a11()
850 fl1 = 1
For j1 = 1 To 121
a20 = a11(j1): If a20 = 0 Then GoTo 855
For j2 = (1 + j1) To 121
If a20 = a11(j2) Then fl1 = 0: Return
Next j2
855 Next j1
Return
' Remove used integers from b1()
900 For i1 = 1 To n32
b1(a(i1)) = 0
Next i1
Return
' Remove used pairs a2() from available integers b1()
910 For i1 = 1 To n32
b1(a2(i1)) = 0: b1(Pr3 - a2(i1)) = 0
Next i1
Return
' Print results (lines)
1640 Cells(n9, 121).Select
For i1 = 1 To 121
Cells(n9, i1).Value = a11(i1)
Next i1
Cells(n9, 122).Value = s11
Cells(n9, 123).Value = j100
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 2 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
s11 = 11 * Cntr3 'MC11
Erase b1
For i1 = 1 To nVar
a1(i1) = i1: b1(i1) = i1
Next i1
m1 = 1: m2 = nVar: pMax = 121
Return
End Sub
