' Constructs 11 x 11 Bordered Magic Squares (Part 2)
' Completes the Border with four Anti Symmetric Magic Rectangles (3 x 5)
' Tested with Office 2007 under Windows 7
Sub Priem11d3()
Dim a1(121), a(121), a3(80), a11(121), b1(121), b(121), c(121)
y = MsgBox("Locked", vbCritical, "Routine Priem11d3")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1: n3 = 0
ShtNm2 = "Lines11"
t1 = Timer
Pr3 = 122: Cntr3 = 61: nVar = 121
s1 = 3 * Cntr3 'MC3
s5 = 5 * Cntr3 'MC5
s11 = 11 * Cntr3 'MC11
For j100 = 2 To 624
' Redefine Integers
Erase b1
For i1 = 1 To nVar
b1(i1) = i1
Next i1
pMax = 121
' Read Semi Magic Corner Squares (3 x 3) and store in a11()
Erase a11
For i1 = 1 To 121
a(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
a11(i1) = a(i1)
Next i1
n31 = 1: n32 = 121: GoSub 900 'Remove used integers from available integers
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
' Generate 3 x 5 Magic Rectangles
b(Cntr3) = Cntr3 'Prevent use of Center Element
t11 = Timer 'Time Out
For j15 = m1 To m2 'a(15)
If b1(a1(j15)) = 0 Then GoTo 150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(16) = Pr3 - a(15): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
For j14 = m1 To m2 'a(14)
If b1(a1(j14)) = 0 Then GoTo 140
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 140
a(14) = a1(j14)
a(17) = Pr3 - a(14): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
For j13 = m1 To m2 'a(13)
If b1(a1(j13)) = 0 Then GoTo 130
If b(a1(j13)) = 0 Then b(a1(j13)) = a1(j13): c(13) = a1(j13) Else GoTo 130
a(13) = a1(j13)
a(18) = Pr3 - a(13): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(19) = Pr3 - a(12): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(11) = s5 - a(12) - a(13) - a(14) - a(15)
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(20) = Pr3 - a(11): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
For j10 = m1 To m2 'a(10)
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(21) = Pr3 - a(10): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(5) = s3 - a(10) - a(15)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(26) = Pr3 - a(5): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
For j9 = m1 To m2 'a(9)
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(22) = Pr3 - a(9): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(4) = s3 - a(9) - a(14)
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(27) = Pr3 - a(4): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
For j8 = m1 To m2 'a(8)
If b1(a1(j8)) = 0 Then GoTo 80
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)
a(23) = Pr3 - a(8): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(3) = s3 - a(8) - a(13)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 30
If b1(a(3)) = 0 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(28) = Pr3 - a(3): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
For j7 = m1 To m2 'a(7)
If b1(a1(j7)) = 0 Then GoTo 70
If b(a1(j7)) = 0 Then b(a1(j7)) = a1(j7): c(7) = a1(j7) Else GoTo 70
a(7) = a1(j7)
a(24) = Pr3 - a(7): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(2) = s3 - a(7) - a(12)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 20
If b1(a(2)) = 0 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(29) = Pr3 - a(2): If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(6) = s5 - a(7) - a(8) - a(9) - a(10)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(25) = Pr3 - a(6): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(1) = s3 - a(6) - a(11)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 10
If b1(a(1)) = 0 Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
a(30) = Pr3 - a(1): If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
n10 = n10 + 1
Select Case n10
Case 1:
a11(4) = a(1): a11(5) = a(2): a11(6) = a(3): a11(7) = a(4): a11(8) = a(5):
a11(15) = a(6): a11(16) = a(7): a11(17) = a(8): a11(18) = a(9): a11(19) = a(10):
a11(26) = a(11): a11(27) = a(12): a11(28) = a(13): a11(29) = a(14): a11(30) = a(15):
a11(92) = a(16): a11(93) = a(17): a11(94) = a(18): a11(95) = a(19): a11(96) = a(20):
a11(103) = a(21): a11(104) = a(22): a11(105) = a(23): a11(106) = a(24): a11(107) = a(25):
a11(114) = a(26): a11(115) = a(27): a11(116) = a(28): a11(117) = a(29): a11(118) = a(30):
n31 = 1: n32 = 15: GoSub 910 'Remove used pairs
Erase b, c: b(Cntr3) = Cntr3: GoTo 150
Case 2:
a11(42) = a(11): a11(43) = a(6): a11(44) = a(1):
a11(53) = a(12): a11(54) = a(7): a11(55) = a(2):
a11(64) = a(13): a11(65) = a(8): a11(66) = a(3):
a11(75) = a(14): a11(76) = a(9): a11(77) = a(4):
a11(86) = a(15): a11(87) = a(10): a11(88) = a(5):
a11(34) = a(26): a11(35) = a(21): a11(36) = a(16):
a11(45) = a(27): a11(46) = a(22): a11(47) = a(17):
a11(56) = a(28): a11(57) = a(23): a11(58) = a(18):
a11(67) = a(29): a11(68) = a(24): a11(69) = a(19):
a11(78) = a(30): a11(79) = a(25): a11(80) = a(20):
GoSub 800: 'Back Check Identical Numbers a11()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 1650 'Print results (squares)
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
End If
Erase b1, b, c: GoTo 1000 'Continue with next Magic Sum
End Select
5 b(c(30)) = 0: c(30) = 0
300 b(c(1)) = 0: c(1) = 0
10 b(c(25)) = 0: c(25) = 0
250 b(c(6)) = 0: c(6) = 0
60 b(c(29)) = 0: c(29) = 0
290 b(c(2)) = 0: c(2) = 0
20 b(c(24)) = 0: c(24) = 0
240 b(c(7)) = 0: c(7) = 0
70 Next j7
b(c(28)) = 0: c(28) = 0
280 b(c(3)) = 0: c(3) = 0
30 b(c(23)) = 0: c(23) = 0
230 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(27)) = 0: c(27) = 0
270 b(c(4)) = 0: c(4) = 0
40 b(c(22)) = 0: c(22) = 0
220 b(c(9)) = 0: c(9) = 0
90 Next j9
b(c(26)) = 0: c(26) = 0
260 b(c(5)) = 0: c(5) = 0
50 b(c(21)) = 0: c(21) = 0
210 b(c(10)) = 0: c(10) = 0
100 Next j10
b(c(20)) = 0: c(20) = 0
200 b(c(11)) = 0: c(11) = 0
110 b(c(19)) = 0: c(19) = 0
190 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(18)) = 0: c(18) = 0
180 b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(17)) = 0: c(17) = 0
170 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(16)) = 0: c(16) = 0
160 b(c(15)) = 0: c(15) = 0
150 Next j15
n3 = 0: n10 = 0
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem11d3")
End
' Double Check Identical Numbers a11()
800 fl1 = 1
For i1 = 1 To 121
a20 = a11(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 121
If a20 = a11(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Remove used integers from b1()
900 For i1 = n31 To n32
b1(a(i1)) = 0
Next i1
Return
' Remove used pairs from b1()
910 For i1 = n31 To n32
b1(a(i1)) = 0: b1(Pr3 - a(i1)) = 0
Next i1
Return
' Print results (lines)
1640 Cells(n9, 122).Select
For i1 = 1 To 121
Cells(n9, i1).Value = a11(i1)
Next i1
Cells(n9, 122).Value = s11
Cells(n9, 123).Value = Rcrd1a
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 = "MC = " + CStr(s11)
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
End Sub
