' Constructs 13 x 13 Composed Magic Squares for Natural Numbers (Part 1)
' Overlapping Sub Squares Order 7 and 3
' Tested with Office 2007 under Windows 7
Sub Prime13d1()
Dim a1(169), a(36), b1(169), b(169), c(36), a13(169)
y = MsgBox("Locked", vbCritical, "Routine Priem13d1")
End
n2 = 0: n3 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
ShtNm2 = "Lines6"
Cntr3 = 85: Pr3 = 2 * Cntr3
s1 = 3 * Pr3 'MC6
s13 = 13 * Cntr3 'MC13
Sheets("Klad1").Select
t1 = Timer
For j101 = 2 To 82
' Redefine variables
GoSub 2010 ' Read first square from sheet "Lines6"
' Generate second square
b(Cntr3) = Cntr3 'Block Center Element
For j36 = m1 To m2 / 2 'a(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
a(36) = a1(j36)
a(1) = s1 / 3 - a(36)
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
For j35 = m1 To m2 'a(35)
If b(a1(j35)) = 0 Then b(a1(j35)) = a1(j35): c(35) = a1(j35) Else GoTo 350
a(35) = a1(j35)
a(2) = s1 / 3 - a(35)
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
For j30 = m1 To m2 'a(30)
If b(a1(j30)) = 0 Then b(a1(j30)) = a1(j30): c(30) = a1(j30) Else GoTo 300
a(30) = a1(j30)
a(29) = 2 * s1 / 3 - a(30) - a(35) - a(36)
If a(29) < a1(m1) Or a(29) > a1(m2) Then GoTo 290
If b1(a(29)) = 0 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(8) = s1 / 3 - a(29)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 80
If b1(a(8)) = 0 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(7) = s1 / 3 - a(30)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
For j34 = m1 To m2 'a(34)
If b(a1(j34)) = 0 Then b(a1(j34)) = a1(j34): c(34) = a1(j34) Else GoTo 340
a(34) = a1(j34)
a(3) = s1 / 3 - a(34)
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
For j33 = m1 To m2 'a(33)
If b(a1(j33)) = 0 Then b(a1(j33)) = a1(j33): c(33) = a1(j33) Else GoTo 330
a(33) = a1(j33)
a(4) = s1 / 3 - a(33)
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
For j28 = m1 To m2 'a(28)
If b(a1(j28)) = 0 Then b(a1(j28)) = a1(j28): c(28) = a1(j28) Else GoTo 280
a(28) = a1(j28)
a(27) = 2 * s1 / 3 - a(28) - a(33) - a(34)
If a(27) < a1(m1) Or a(27) > a1(m2) Then GoTo 270
If b1(a(27)) = 0 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(10) = s1 / 3 - a(27)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 100
If b1(a(10)) = 0 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(9) = s1 / 3 - a(28)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 90
If b1(a(9)) = 0 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j32 = m1 To m2 'a(32)
If b(a1(j32)) = 0 Then b(a1(j32)) = a1(j32): c(32) = a1(j32) Else GoTo 320
a(32) = a1(j32)
a(31) = s1 - a(32) - a(33) - a(34) - a(35) - a(36)
If a(31) < a1(m1) Or a(31) > a1(m2) Then GoTo 310
If b1(a(31)) = 0 Then GoTo 310
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(6) = s1 / 3 - a(31)
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(5) = s1 / 3 - a(32)
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
For j26 = m1 To m2 'a(26)
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)
a(25) = -s1 / 3 - a(26) + a(33) + a(34) + a(35) + a(36)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(12) = s1 / 3 - a(25)
If a(12) < a1(m1) Or a(12) > a1(m2) Then GoTo 120
If b1(a(12)) = 0 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(11) = s1 / 3 - a(26)
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
For j24 = m1 To m2 'a(24)
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
a(13) = s1 / 3 - a(24)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130
If b1(a(13)) = 0 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j23 = m1 To m2 'a(23)
If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
a(23) = a1(j23)
a(22) = 5 * s1 / 6 - a(23) - a(24) - a(28) - a(34)
If a(22) < a1(m1) Or a(22) > a1(m2) Then GoTo 220
If b1(a(22)) = 0 Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = s1 / 6 - a(23) - a(24) + a(28) + a(34)
If a(21) < a1(m1) Or a(21) > a1(m2) Then GoTo 210
If b1(a(21)) = 0 Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = 2 * s1 / 3 + a(23) - a(26) - a(30) - a(32) - a(36)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 200
If b1(a(20)) = 0 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = -2 * s1 / 3 + a(24) + a(26) + a(30) + a(32) + a(36)
If a(19) < a1(m1) Or a(19) > a1(m2) Then GoTo 190
If b1(a(19)) = 0 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(18) = s1 / 3 - a(19)
If a(18) < a1(m1) Or a(18) > a1(m2) Then GoTo 180
If b1(a(18)) = 0 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(17) = s1 / 3 - a(20)
If a(17) < a1(m1) Or a(17) > a1(m2) Then GoTo 170
If b1(a(17)) = 0 Then GoTo 170
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(16) = s1 / 3 - a(21)
If a(16) < a1(m1) Or a(16) > a1(m2) Then GoTo 160
If b1(a(16)) = 0 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(15) = s1 / 3 - a(22)
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(14) = s1 / 3 - a(23)
If a(14) < a1(m1) Or a(14) > a1(m2) Then GoTo 140
If b1(a(14)) = 0 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a13(99) = a(1): a13(100) = a(2): a13(101) = a(3): a13(102) = a(4): a13(103) = a(5): a13(104) = a(6):
a13(112) = a(7): a13(113) = a(8): a13(114) = a(9): a13(115) = a(10): a13(116) = a(11): a13(117) = a(12):
a13(125) = a(13): a13(126) = a(14): a13(127) = a(15): a13(128) = a(16): a13(129) = a(17): a13(130) = a(18):
a13(138) = a(19): a13(139) = a(20): a13(140) = a(21): a13(141) = a(22): a13(142) = a(23): a13(143) = a(24):
a13(151) = a(25): a13(152) = a(26): a13(153) = a(27): a13(154) = a(28): a13(155) = a(29): a13(156) = a(30):
a13(164) = a(31): a13(165) = a(32): a13(166) = a(33): a13(167) = a(34): a13(168) = a(35): a13(169) = a(36):
GoSub 800 'Double Check Identical Integers a13()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 2650 'Print Composed Squares a13()
' n9 = n9 + 1: GoSub 2645 'Print Composed Lines a13()
End If
Erase b1, b, c: GoTo 500 'Print only first square
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(17)) = 0: c(17) = 0
170 b(c(18)) = 0: c(18) = 0
180 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(13)) = 0: c(13) = 0
130 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 b(c(25)) = 0: c(25) = 0
250 b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 b(c(27)) = 0: c(27) = 0
270 b(c(28)) = 0: c(28) = 0
280 Next j28
b(c(4)) = 0: c(4) = 0
40 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(3)) = 0: c(3) = 0
30 b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(2)) = 0: c(2) = 0
20 b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(1)) = 0: c(1) = 0
10 b(c(36)) = 0: c(36) = 0
360 Next j36
500 Next j101
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine PrimeSqrs13d1")
End
' Print results (selected numbers)
2645 For i1 = 1 To 169
Cells(n9, i1).Value = a13(i1)
Next i1
Cells(n9, 170).Value = j101
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 2 Then
n2 = 1: k1 = k1 + 14: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 14
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = j101
i3 = 0
For i1 = 1 To 13
For i2 = 1 To 13
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a13(i3)
Next i2
Next i1
Return
' Redefine Varaibles
2010 nVar1 = 169
For i1 = 1 To nVar1
a1(i1) = i1
Next i1
m1 = 1: m2 = nVar1
pMax = a1(m2)
Erase b1
For i1 = m1 To m2: b1(a1(i1)) = a1(i1): Next i1
' Read Corner Square 6 x 6
For i1 = 1 To 36
a(i1) = Sheets(ShtNm2).Cells(j101, i1).Value
Next i1
n10 = 0: n53 = 36: GoSub 910 'Remove used integers from available integers
Erase a13
a13(1) = a(1): a13(2) = a(2): a13(3) = a(3): a13(4) = a(4): a13(5) = a(5): a13(6) = a(6):
a13(14) = a(7): a13(15) = a(8): a13(16) = a(9): a13(17) = a(10): a13(18) = a(11): a13(19) = a(12):
a13(27) = a(13): a13(28) = a(14): a13(29) = a(15): a13(30) = a(16): a13(31) = a(17): a13(32) = a(18):
a13(40) = a(19): a13(41) = a(20): a13(42) = a(21): a13(43) = a(22): a13(44) = a(23): a13(45) = a(24):
a13(53) = a(25): a13(54) = a(26): a13(55) = a(27): a13(56) = a(28): a13(57) = a(29): a13(58) = a(30):
a13(66) = a(31): a13(67) = a(32): a13(68) = a(33): a13(69) = a(34): a13(70) = a(35): a13(71) = a(36):
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
Return
' Double Check Identical Numbers a13()
800 fl1 = 1
For i1 = 1 To 169
a20 = a13(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 169
If a20 = a13(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Remove used integers a() from available integers b1()
910 For i1 = 1 To n53
b1(a(i1)) = 0
Next i1
Return
End Sub
