' Generates Inlaid Magic Squares of order 11, Prime Numbers (Border)
' Tested with Office 365 under Windows 10
Sub MgcSqr11k1()
Dim a1(1690), a(121), b1(50169), b(50169), c(121), s(4)
Dim a9(811)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr11k1")
End
n1 = 0: n2 = 0: n3 = 0: k1 = 1: k2 = 1: n9 = 0: n10 = 0
ShtNm1 = "Pairs7"
ShtNm2 = "CntrLns11"
Sheets("Klad1").Select
t1 = Timer
For j100 = 543 To 543 'Test Case = 543
Rcrd1a = j100
GoSub 2000 'Define variables
''s(3) = Sheets(ShtNm2).Cells(j100, 84).Value
''s(4) = Sheets(ShtNm2).Cells(j100, 85).Value
s(3) = 20432 'Test Case
s(4) = 25945 'Test Case
s(1) = 10 * s11 / 11 - s(4)
s(2) = 8 * s11 / 11 - s(3)
' Create Border
t11 = Timer 'Time Out
For j121 = (m2 - 1) / 2 To m2 'a(121)
If b(a1(j121)) = 0 Then b(a1(j121)) = a1(j121): c(121) = a1(j121) Else GoTo 1210
a(121) = a1(j121)
a(1) = 2 * s11 / 11 - a(121): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j120 = m2 To m1 Step -1 'a(120)
If b(a1(j120)) = 0 Then b(a1(j120)) = a1(j120): c(120) = a1(j120) Else GoTo 1200
a(120) = a1(j120)
a(112) = -s11 / 11 + a(120) - s(3) + s(4)
If a(112) < a1(m1) Or a(112) > a1(m2) Then GoTo 1120
If b1(a(112)) = 0 Then GoTo 1120
If b(a(112)) = 0 Then b(a(112)) = a(112): c(112) = a(112) Else GoTo 1120
a(10) = 2 * s11 / 11 - a(112): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(2) = 2 * s11 / 11 - a(120): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j119 = m2 To m1 Step -1 'a(119)
If b(a1(j119)) = 0 Then b(a1(j119)) = a1(j119): c(119) = a1(j119) Else GoTo 1190
a(119) = a1(j119)
a(113) = -s11 / 11 + a(119) - s(3) + s(4)
If a(113) < a1(m1) Or a(113) > a1(m2) Then GoTo 1130
If b1(a(113)) = 0 Then GoTo 1130
If b(a(113)) = 0 Then b(a(113)) = a(113): c(113) = a(113) Else GoTo 1130
a(9) = 2 * s11 / 11 - a(113): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(3) = 2 * s11 / 11 - a(119): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j118 = m1 To m2 'a(118)
If b(a1(j118)) = 0 Then b(a1(j118)) = a1(j118): c(118) = a1(j118) Else GoTo 1180
a(118) = a1(j118)
a(114) = -s11 / 11 + a(118) - s(3) + s(4)
If a(114) < a1(m1) Or a(114) > a1(m2) Then GoTo 1140
If b1(a(114)) = 0 Then GoTo 1140
If b(a(114)) = 0 Then b(a(114)) = a(114): c(114) = a(114) Else GoTo 1140
a(8) = 2 * s11 / 11 - a(114): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(4) = 2 * s11 / 11 - a(118): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j117 = m1 To m2 'a(117)
If b(a1(j117)) = 0 Then b(a1(j117)) = a1(j117): c(117) = a1(j117) Else GoTo 1170
a(117) = a1(j117)
a(115) = -s11 / 11 + a(117) - s(3) + s(4)
If a(115) < a1(m1) Or a(115) > a1(m2) Then GoTo 1150
If b1(a(115)) = 0 Then GoTo 1150
If b(a(115)) = 0 Then b(a(115)) = a(115): c(115) = a(115) Else GoTo 1150
a(7) = 2 * s11 / 11 - a(115): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(5) = 2 * s11 / 11 - a(117): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j116 = m1 To m2 'a(116)
If b(a1(j116)) = 0 Then b(a1(j116)) = a1(j116): c(116) = a1(j116) Else GoTo 1160
a(116) = a1(j116)
a(111) = 15 * s11 / 11 - a(116) - 2*a(117) - 2*a(118) - 2*a(119) - 2*a(120) - a(121) + 4*s(3) - 4*s(4)
If a(111) < a1(m1) Or a(111) > a1(m2) Then GoTo 1110
If b1(a(111)) = 0 Then GoTo 1110
If b(a(111)) = 0 Then b(a(111)) = a(111): c(111) = a(111) Else GoTo 1110
a(11) = 2 * s11 / 11 - a(111): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(6) = 2 * s11 / 11 - a(116): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j110 = m2 To m1 Step -1 'a(110)
If b(a1(j110)) = 0 Then b(a1(j110)) = a1(j110): c(110) = a1(j110) Else GoTo 1100
a(110) = a1(j110)
a(100) = s11 - a(110) - s(3) - s(4)
If a(100) < a1(m1) Or a(100) > a1(m2) Then GoTo 1000
If b1(a(100)) = 0 Then GoTo 1000
If b(a(100)) = 0 Then b(a(100)) = a(100): c(100) = a(100) Else GoTo 1000
a(22) = 2 * s11 / 11 - a(100): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(12) = 2 * s11 / 11 - a(110): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
''n9 = n9 + 1: GoSub 1650: End
For j99 = m2 To m1 Step -1 'a(99)
If b(a1(j99)) = 0 Then b(a1(j99)) = a1(j99): c(99) = a1(j99) Else GoTo 990
a(99) = a1(j99)
a(89) = s11 - a(99) - s(3) - s(4)
If a(89) < a1(m1) Or a(89) > a1(m2) Then GoTo 890
If b1(a(89)) = 0 Then GoTo 890
If b(a(89)) = 0 Then b(a(89)) = a(89): c(89) = a(89) Else GoTo 890
a(33) = 2 * s11 / 11 - a(89): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(23) = 2 * s11 / 11 - a(99): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
For j88 = m1 To m2 'a(88)
If b(a1(j88)) = 0 Then b(a1(j88)) = a1(j88): c(88) = a1(j88) Else GoTo 880
a(88) = a1(j88)
a(78) = s11 - a(88) - s(3) - s(4)
If a(78) < a1(m1) Or a(78) > a1(m2) Then GoTo 780
If b1(a(78)) = 0 Then GoTo 780
If b(a(78)) = 0 Then b(a(78)) = a(78): c(78) = a(78) Else GoTo 780
a(44) = 2 * s11 / 11 - a(78): If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(34) = 2 * s11 / 11 - a(88): If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
For j77 = m1 To m2 'a(77)
If b(a1(j77)) = 0 Then b(a1(j77)) = a1(j77): c(77) = a1(j77) Else GoTo 770
a(77) = a1(j77)
a(67) = s11 - a(77) - s(3) - s(4)
If a(67) < a1(m1) Or a(67) > a1(m2) Then GoTo 670
If b1(a(67)) = 0 Then GoTo 670
If b(a(67)) = 0 Then b(a(67)) = a(67): c(67) = a(67) Else GoTo 670
a(66) = 60 * s11 / 11 - 2*a(77) - 2*a(88) - 2*a(99) - 2*a(110) - a(116) - 2*a(117) - 2*a(118) +
- 2 * a(119) - 2 * a(120) - 2 * a(121) - 8 * s(4)
If a(66) < a1(m1) Or a(66) > a1(m2) Then GoTo 660
If b1(a(66)) = 0 Then GoTo 660
If b(a(66)) = 0 Then b(a(66)) = a(66): c(66) = a(66) Else GoTo 660
a(56) = 2 * s11 / 11 - a(66): If b(a(56)) = 0 Then b(a(56)) = a(56): c(56) = a(56) Else GoTo 560
a(55) = 2 * s11 / 11 - a(67): If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
a(45) = 2 * s11 / 11 - a(77): If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
GoSub 1300: If fl1 = 0 Then GoTo 5 'Back Check Identical Numbers
n9 = n9 + 1: GoSub 1650 'Print Square
Erase b, c: GoTo 500 'Print only one square
5
b(c(45)) = 0: c(45) = 0
450 b(c(55)) = 0: c(55) = 0
550 b(c(56)) = 0: c(56) = 0
560 b(c(66)) = 0: c(66) = 0
660 b(c(67)) = 0: c(67) = 0
670 b(c(77)) = 0: c(77) = 0
770 Next j77
b(c(34)) = 0: c(34) = 0
340 b(c(44)) = 0: c(44) = 0
440 b(c(78)) = 0: c(78) = 0
780 b(c(88)) = 0: c(88) = 0
880 Next j88
b(c(23)) = 0: c(23) = 0
230 b(c(33)) = 0: c(33) = 0
330 b(c(89)) = 0: c(89) = 0
890 b(c(99)) = 0: c(99) = 0
990 Next j99
b(c(12)) = 0: c(12) = 0
120 b(c(22)) = 0: c(22) = 0
220 b(c(100)) = 0: c(100) = 0
1000 b(c(110)) = 0: c(110) = 0
1100 Next j110
b(c(6)) = 0: c(6) = 0
60 b(c(11)) = 0: c(11) = 0
110 b(c(111)) = 0: c(111) = 0
1110 b(c(116)) = 0: c(116) = 0
1160 Next j116
b(c(5)) = 0: c(5) = 0
50 b(c(7)) = 0: c(7) = 0
70 b(c(115)) = 0: c(115) = 0
1150 b(c(117)) = 0: c(117) = 0
1170 Next j117
b(c(4)) = 0: c(4) = 0
40 b(c(8)) = 0: c(8) = 0
80 b(c(114)) = 0: c(114) = 0
1140 b(c(118)) = 0: c(118) = 0
1180 Next j118
b(c(3)) = 0: c(3) = 0
30 b(c(9)) = 0: c(9) = 0
90 b(c(113)) = 0: c(113) = 0
1130 b(c(119)) = 0: c(119) = 0
1190 Next j119
b(c(2)) = 0: c(2) = 0
20 b(c(10)) = 0: c(10) = 0
100 b(c(112)) = 0: c(112) = 0
1120 b(c(120)) = 0: c(120) = 0
1200 Next j120
b(c(1)) = 0: c(1) = 0
10 b(c(121)) = 0: c(121) = 0
1210 Next j121
500 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s11)
y = MsgBox(t10, 0, "Routine MgcSqr11k1")
End
' Remove used pairs from b1()
950 For i1 = 1 To n32
b1(a9(i1)) = 0
If (Pr11 - a9(i1)) > 0 Then
b1(Pr11 - a9(i1)) = 0 'Complement
End If
Next i1
Return
' Define Variables
2000 fl1 = 1
' Start Reading Data ShtNm2
'' Rcrd1a = Sheets(ShtNm2).Cells(j100, 86).Value
' Read Prime Numbers From Sheet ShtNm1
Pr11 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value 'PairSum
s11 = 11 * Pr11 / 2
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
Erase b1
For j1 = 1 To nVar
x = Sheets(ShtNm1).Cells(Rcrd1a, 9 + j1).Value
b1(x) = x: a1(j1) = x
Next j1
pMax = Sheets(ShtNm1).Cells(Rcrd1a, 9 + nVar).Value
m1 = 1: m2 = nVar
Return
' Read Inlaid Squares 4 x 4 / 5 x 5
For i1 = 1 To 81
a9(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
Next i1
n32 = 81: GoSub 950 'Remove used primes from available primes
Erase a
a(13) = a9(1): a(14) = a9(2): a(15) = a9(3): a(16) = a9(4): a(17) = a9(5): a(18) = a9(6): a(19) = a9(7):
a(20) = a9(8): a(21) = a9(9):
a(24) = a9(10): a(25) = a9(11): a(26) = a9(12): a(27) = a9(13): a(28) = a9(14): a(29) = a9(15): a(30) = a9(16):
a(31) = a9(17): a(32) = a9(18):
a(35) = a9(19): a(36) = a9(20): a(37) = a9(21): a(38) = a9(22): a(39) = a9(23): a(40) = a9(24): a(41) = a9(25):
a(42) = a9(26): a(43) = a9(27):
a(46) = a9(28): a(47) = a9(29): a(48) = a9(30): a(49) = a9(31): a(50) = a9(32): a(51) = a9(33): a(52) = a9(34):
a(53) = a9(35): a(54) = a9(36):
a(57) = a9(37): a(58) = a9(38): a(59) = a9(39): a(60) = a9(40): a(61) = a9(41): a(62) = a9(42): a(63) = a9(43):
a(64) = a9(44): a(65) = a9(45):
a(68) = a9(46): a(69) = a9(47): a(70) = a9(48): a(71) = a9(49): a(72) = a9(50): a(73) = a9(51): a(74) = a9(52):
a(75) = a9(53): a(76) = a9(54):
a(79) = a9(55): a(80) = a9(56): a(81) = a9(57): a(82) = a9(58): a(83) = a9(59): a(84) = a9(60): a(85) = a9(61):
a(86) = a9(62): a(87) = a9(63):
a(90) = a9(64): a(91) = a9(65): a(92) = a9(66): a(93) = a9(67): a(94) = a9(68): a(95) = a9(69): a(96) = a9(70):
a(97) = a9(71): a(98) = a9(72):
a(101) = a9(73): a(102) = a9(74): a(103) = a9(75): a(104) = a9(76): a(105) = a9(77): a(106) = a9(78): a(107) = a9(79):
a(108) = a9(80): a(109) = a9(81):
Erase a9
' 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
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
Return
' Exclude solutions with identical numbers
1300 fl1 = 1
For j10 = 1 To 121
c2 = a(j10): If c2 = 0 Then GoTo 1310
For j20 = (1 + j10) To 121
If c2 = a(j20) Then fl1 = 0: Return
Next j20
1310 Next j10
Return
' Print results (lines)
1640 ''Cells(n9, 122).Select
For i1 = 1 To 121
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 122).Value = s11
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 3 Then
n2 = 1: k1 = k1 + 12: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 12
End If
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = s11
i3 = 0
For i1 = 1 To 11
For i2 = 1 To 11
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
