' Constructs 9 x 9 Magic Squares with Overlapping Subsquares (Distinct Prime Numbers):
' - Transforms pairs of Prime Number Ultra Magic Squares (5 x 5)
' - Generates additional Prime Number Pan Magic Squares (4 x 4)
' Tested with Office 2007 under Windows 7
Sub Priem4e()
Dim a1(1944), a(81), b1(43300), b(43300), c(16)
Dim a4(16), b5(25), c5(25), d4(16) 'Sub Squares
y = MsgBox("Locked", vbCritical, "Routine Priem4e")
End
n2 = 0: n3 = 0: k1 = 1: k2 = 1: n9 = 0: n10 = 0
Sht1 = "Pairs7"
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j100 = 2 To 49 ''660
' Start Reading Data PM5a/PM5b
Rcrd1a = Sheets("PM5a").Cells(j100, 28).Value
MC5a = Sheets("PM5a").Cells(j100, 26).Value
Rcrd1b = Sheets("PM5b").Cells(j100, 28).Value
MC5b = Sheets("PM5b").Cells(j100, 26).Value
If Rcrd1a <> Rcrd1b Or MC5a <> MC5b Then
y = MsgBox("Conflict in Data", vbCritical, "Read PM5a/b")
End
End If
' Read Prime Numbers From Sheet Sht1
s1 = 2 * Sheets(Sht1).Cells(Rcrd1a, 1).Value 'PM4
s2 = 9 * s1 / 4 'PM9
nVar = Sheets(Sht1).Cells(Rcrd1a, 9).Value
m1 = 1: m2 = nVar
For i1 = m1 To m2
a1(i1) = Sheets(Sht1).Cells(Rcrd1a, i1 + 9).Value
Next i1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Read Prime Numbers used for 2 x PM5
For i1 = 1 To 25
a(i1) = Sheets("PM5a").Cells(j100, i1).Value
Next i1
GoSub 700 'Fill b5()
For i1 = 1 To 25
a(i1) = Sheets("PM5b").Cells(j100, i1).Value
Next i1
GoSub 750 'Fill c5()
GoSub 950 'Remove used primes from available primes
Erase a 'Clear Scratch Area
' Generate Prime Number Pan Magic Squares (4 x 4)
For j16 = m1 To m2 'a(16)
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
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)
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(13) = s1 - a(14) - a(15) - a(16)
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 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(11) = s1 - a(12) - a(15) - a(16)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 70
If b1(a(11)) = 0 Then GoTo 70
a(10) = a(12) - a(14) + a(16)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 70
If b1(a(10)) = 0 Then GoTo 70
a(9) = -a(12) + a(14) + a(15)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 70
If b1(a(9)) = 0 Then GoTo 70
a(8) = 0.5 * s1 - a(14)
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 70
If b1(a(8)) = 0 Then GoTo 70
a(7) = -0.5 * s1 + a(14) + a(15) + a(16)
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70:
If b1(a(7)) = 0 Then GoTo 70
a(6) = 0.5 * s1 - a(16)
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 70:
If b1(a(6)) = 0 Then GoTo 70
a(5) = 0.5 * s1 - a(15)
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 70:
If b1(a(5)) = 0 Then GoTo 70
a(4) = 0.5 * s1 - a(12) + a(14) - a(16)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 70:
If b1(a(4)) = 0 Then GoTo 70
a(3) = 0.5 * s1 + a(12) - a(14) - a(15)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 70:
If b1(a(3)) = 0 Then GoTo 70
a(2) = 0.5 * s1 - a(12)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 70:
If b1(a(2)) = 0 Then GoTo 70
a(1) = -0.5 * s1 + a(12) + a(15) + a(16)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 70:
If b1(a(1)) = 0 Then GoTo 70
' Exclude solutions with identical numbers (PM4)
n8 = 16: GoSub 800: If fl1 = 0 Then GoTo 70
n10 = n10 + 1
Select Case n10
Case 1
For i1 = 1 To 16: a4(i1) = a(i1): Next i1
GoSub 900 'Remove used primes from available primes
Erase b, c: GoTo 160
Case 2
For i1 = 1 To 16: d4(i1) = a(i1): Next i1
GoSub 600 'Compose Main Square
n8 = 81: GoSub 800 'Double Check Identical Integers
If fl1 = 1 Then
n9 = n9 + 1: GoSub 650 'Print Composed Squares
End If
End Select
If n10 = 2 Then n10 = 0: Erase b, c: GoTo 10 'Only two squares required
70 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(16)) = 0: c(16) = 0
160 Next j16
n10 = 0
10 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine Priem4e")
End
' Compose Main Square
600 a(1) = a4(1): a(2) = a4(2): a(3) = a4(3): a(4) = a4(4): a(5) = b5(1): a(6) = b5(2): a(7) = b5(3): a(8) = b5(4): a(9) = b5(5):
a(10) = a4(5): a(11) = a4(6): a(12) = a4(7): a(13) = a4(8): a(14) = b5(6): a(15) = b5(7): a(16) = b5(8): a(17) = b5(9): a(18) = b5(10):
a(19) = a4(9): a(20) = a4(10): a(21) = a4(11): a(22) = a4(12): a(23) = b5(11): a(24) = b5(12): a(25) = b5(13): a(26) = b5(14): a(27) = b5(15):
a(28) = a4(13): a(29) = a4(14): a(30) = a4(15): a(31) = a4(16): a(32) = b5(16): a(33) = b5(17): a(34) = b5(18): a(35) = b5(19): a(36) = b5(20):
a(37) = c5(1): a(38) = c5(2): a(39) = c5(3): a(40) = c5(4): a(41) = b5(21): a(42) = b5(22): a(43) = b5(23): a(44) = b5(24): a(45) = b5(25):
a(46) = c5(6): a(47) = c5(7): a(48) = c5(8): a(49) = c5(9): a(50) = c5(10): a(51) = d4(1): a(52) = d4(2): a(53) = d4(3): a(54) = d4(4):
a(55) = c5(11): a(56) = c5(12): a(57) = c5(13): a(58) = c5(14): a(59) = c5(15): a(60) = d4(5): a(61) = d4(6): a(62) = d4(7): a(63) = d4(8):
a(64) = c5(16): a(65) = c5(17): a(66) = c5(18): a(67) = c5(19): a(68) = c5(20): a(69) = d4(9): a(70) = d4(10): a(71) = d4(11): a(72) = d4(12):
a(73) = c5(21): a(74) = c5(22): a(75) = c5(23): a(76) = c5(24): a(77) = c5(25): a(78) = d4(13): a(79) = d4(14): a(80) = d4(15): a(81) = d4(16):
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 3 Then
n2 = 1: k1 = k1 + 10: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 10
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s2)
i3 = 0
For i1 = 1 To 9
For i2 = 1 To 9
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Transform Ultra Magic Squares into b5() and c5()
700 b5(1) = a(18): b5(2) = a(19): b5(3) = a(20): b5(4) = a(16): b5(5) = a(17):
b5(6) = a(23): b5(7) = a(24): b5(8) = a(25): b5(9) = a(21): b5(10) = a(22):
b5(11) = a(3): b5(12) = a(4): b5(13) = a(5): b5(14) = a(1): b5(15) = a(2):
b5(16) = a(8): b5(17) = a(9): b5(18) = a(10): b5(19) = a(6): b5(20) = a(7):
b5(21) = a(13): b5(22) = a(14): b5(23) = a(15): b5(24) = a(11): b5(25) = a(12):
Return
750 c5(1) = a(14): c5(2) = a(15): c5(3) = a(11): c5(4) = a(12): c5(5) = a(13):
c5(6) = a(19): c5(7) = a(20): c5(8) = a(16): c5(9) = a(17): c5(10) = a(18):
c5(11) = a(24): c5(12) = a(25): c5(13) = a(21): c5(14) = a(22): c5(15) = a(23):
c5(16) = a(4): c5(17) = a(5): c5(18) = a(1): c5(19) = a(2): c5(20) = a(3):
c5(21) = a(9): c5(22) = a(10): c5(23) = a(6): c5(24) = a(7): c5(25) = a(8):
Return
' Exclude solutions with identical numbers (PM4)
800 fl1 = 1
For j1 = 1 To n8
a2 = a(j1)
For j2 = (1 + j1) To n8
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Remove used primes from available primes (PM4)
900 For i1 = 1 To 16
b1(a(i1)) = 0
Next i1
Return
' Remove used primes from available primes (2 x PM5)
950 For i1 = 1 To 25
b1(b5(i1)) = 0: b1(c5(i1)) = 0
Next i1
Return
End Sub
