' Constructs Prime Number Composed Magic Squares of Order 15
' Tested with Office 2007 under Windows 7
Sub PriemG15()
Dim a1(2448), a(64), a15(225), b1(43300), b(43300), c(64), Crnr3(2)
y = MsgBox("Locked", vbCritical, "Routine PriemG15")
End
Sheets("Klad1").Select
n5 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "Pairs7"
ShtNm2 = "Sqrs11"
t1 = Timer
For j100 = 2 To 16
' Start Reading Data ShtNm2
Rcrd1a = Sheets(ShtNm2).Cells(j100, 227).Value
MC15 = Sheets(ShtNm2).Cells(j100, 226).Value
' Read Prime Numbers From Sheet ShtNm1
Pr3 = Sheets(ShtNm1).Cells(Rcrd1a, 1).Value 'PairSum
Cntr3 = Sheets(ShtNm1).Cells(Rcrd1a, 6).Value 'Center Element
s3 = 3 * Cntr3 'MC3
s5 = 5 * Cntr3 'MC5
s6 = 6 * Cntr3 'MC6
s9 = 9 * Cntr3 'MC9
s15 = 15 * Cntr3 'MC15
nVar = Sheets(ShtNm1).Cells(Rcrd1a, 9).Value
If nVar < 225 Then GoTo 1000
If MC15 <> s15 Then
y = MsgBox("Conflict in Data", vbCritical, "Read " + ShtNm2 + " " + CStr(j100))
End
End If
Erase b1
For j1 = 1 To nVar
x = Sheets(ShtNm1).Cells(Rcrd1a, 9 + j1).Value
b1(x) = x
Next j1
pMax = Sheets(ShtNm1).Cells(Rcrd1a, 9 + nVar).Value
' Read Composed Magic Squares (11 x 11)
' Store in a15() and Remove used pairs from b1()
For i1 = 1 To 225
a15(i1) = Sheets(ShtNm2).Cells(j100, i1).Value
b1(a15(i1)) = 0
Next i1
' 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
' Complete 9 x 9 Eccentric Magic Squares
Crnr3(1) = a15(39) + a15(55) + a15(71) + a15(87) + a15(103) ' Square 1
Crnr3(2) = a15(123) + a15(139) + a15(155) + a15(171) + a15(187) ' Square 2
i35 = 1
For n10 = 1 To 2
Erase a, b, c
GoSub 3000: If fl1 = 0 Then GoTo 1000
GoSub 2000: If fl1 = 0 Then GoTo 1000
Select Case n10
Case 1:
a15(7) = a(10): a15(8) = a(15): a15(9) = a(19): a15(10) = a(22): a15(11) = a(23): a15(12) = a(24): a15(13) = a(8):
a15(22) = a(14): a15(23) = a(11): a15(24) = a(21): a15(25) = a(25): a15(26) = a(26): a15(27) = a(27): a15(28) = a(2):
a15(14) = a(9): a15(15) = a(7):
a15(29) = a(3): a15(30) = a(1):
a15(44) = a(6): a15(45) = a(4):
a15(59) = a(31): a15(60) = a(28):
a15(74) = a(32): a15(75) = a(29):
a15(89) = a(33): a15(90) = a(30):
a15(104) = a(20): a15(105) = a(18):
a15(119) = a(12): a15(120) = a(16):
a15(134) = a(17): a15(135) = a(13):
n32 = 33: GoSub 900 'Remove used primes from available primes
i35 = 2
Case 2:
a15(91) = a(13): a15(92) = a(17):
a15(106) = a(16): a15(107) = a(12):
a15(121) = a(18): a15(122) = a(20):
a15(136) = a(30): a15(137) = a(33):
a15(151) = a(29): a15(152) = a(32):
a15(166) = a(28): a15(167) = a(31):
a15(181) = a(4): a15(182) = a(6):
a15(196) = a(1): a15(197) = a(3):
a15(211) = a(7): a15(212) = a(9):
a15(198) = a(2): a15(199) = a(27): a15(200) = a(26): a15(201) = a(25): a15(202) = a(21): a15(203) = a(11): a15(204) = a(14):
a15(213) = a(8): a15(214) = a(24): a15(215) = a(23): a15(216) = a(22): a15(217) = a(19): a15(218) = a(15): a15(219) = a(10):
n32 = 33: GoSub 900 'Remove used primes from available primes
End Select
Next n10
' Complete 6 x 6 Eccentric Magic Squares
Crnr3(1) = a15(34) + a15(48) ' Square 1
Crnr3(2) = a15(178) + a15(192) ' Square 2
i35 = 1
For n10 = 1 To 2
Erase a, b, c
GoSub 6000: If fl1 = 0 Then GoTo 1000
Select Case n10
Case 1:
a15(1) = a(20): a15(2) = a(19): a15(3) = a(18): a15(4) = a(17): a15(5) = a(6): a15(6) = a(1):
a15(16) = a(24): a15(17) = a(23): a15(18) = a(22): a15(19) = a(21): a15(20) = a(2): a15(21) = a(5):
a15(31) = a(25): a15(32) = a(27):
a15(46) = a(26): a15(47) = a(28):
a15(61) = a(7): a15(62) = a(3):
a15(76) = a(4): a15(77) = a(8):
n32 = 28: GoSub 900 'Remove used primes from available primes
i35 = 2
Case 2:
a15(149) = a(8): a15(150) = a(4):
a15(164) = a(3): a15(165) = a(7):
a15(179) = a(28): a15(180) = a(26):
a15(194) = a(27): a15(195) = a(25):
a15(205) = a(5): a15(206) = a(2): a15(207) = a(21): a15(208) = a(22): a15(209) = a(23): a15(210) = a(24):
a15(220) = a(1): a15(221) = a(6): a15(222) = a(17): a15(223) = a(18): a15(224) = a(19): a15(225) = a(20):
GoSub 800: 'Back Check Identical Numbers a15()
If fl1 = 1 Then
n9 = n9 + 1: GoSub 1650 'Print results (squares)
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
End If
End Select
Next n10
Erase b1, b, c
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine PriemG15")
End
' Determine Main Diagonal and Remaining Pairs
6000 fl1 = 1
For j1 = m1 To m2
If b1(a1(j1)) = 0 Then GoTo 6010
If b(a1(j1)) = 0 Then b(a1(j1)) = a1(j1): c(1) = a1(j1) Else GoTo 6010
a(1) = a1(j1)
a(5) = Pr3 - a(1): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 6050
For j2 = m1 To m2
If b1(a1(j2)) = 0 Then GoTo 6020
If b(a1(j2)) = 0 Then b(a1(j2)) = a1(j2): c(2) = a1(j2) Else GoTo 6020
a(2) = a1(j2)
a(6) = Pr3 - a(2): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 6060
For j3 = m1 To m2
If b1(a1(j3)) = 0 Then GoTo 6030
If b(a1(j3)) = 0 Then b(a1(j3)) = a1(j3): c(3) = a1(j3) Else GoTo 6030
a(3) = a1(j3)
a(7) = Pr3 - a(3): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 6070
a(4) = s6 - a(3) - a(2) - a(1) - Crnr3(i35)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 6040:
If b1(a(4)) = 0 Then GoTo 6040
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 6040
a(8) = Pr3 - a(4): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 6080
' Determine remainder of the pairs
For j17 = m1 To m2 'a(17)
If b1(a1(j17)) = 0 Then GoTo 6170
If b(a1(j17)) = 0 Then b(a1(j17)) = a1(j17): c(17) = a1(j17) Else GoTo 6170
a(17) = a1(j17)
a(21) = Pr3 - a(17): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 6210
For j18 = m1 To m2
If b1(a1(j18)) = 0 Then GoTo 6180
If b(a1(j18)) = 0 Then b(a1(j18)) = a1(j18): c(18) = a1(j18) Else GoTo 6180
a(18) = a1(j18)
a(22) = Pr3 - a(18): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 6220
For j19 = m1 To m2
If b1(a1(j19)) = 0 Then GoTo 6190
If b(a1(j19)) = 0 Then b(a1(j19)) = a1(j19): c(19) = a1(j19) Else GoTo 6190
a(19) = a1(j19)
a(24) = Pr3 - a(19): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 6240
a(20) = s6 - a(19) - a(18) - a(17) - a(6) - a(1)
If a(20) < a1(m1) Or a(20) > a1(m2) Then GoTo 6200:
If b1(a(20)) = 0 Then GoTo 6200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 6200
a(23) = Pr3 - a(20): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 6230
For j25 = m1 To m2
If b1(a1(j25)) = 0 Then GoTo 6250
If b(a1(j25)) = 0 Then b(a1(j25)) = a1(j25): c(25) = a1(j25) Else GoTo 6250
a(25) = a1(j25)
a(27) = Pr3 - a(25): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 6270
a(26) = s6 - a(25) - a(24) - a(20) - a(7) - a(4)
If a(26) < a1(m1) Or a(26) > a1(m2) Then GoTo 6260:
If b1(a(26)) = 0 Then GoTo 6260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 6260
a(28) = Pr3 - a(26): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 6280
Return
b(c(28)) = 0: c(28) = 0
6280 b(c(26)) = 0: c(26) = 0
6260 b(c(27)) = 0: c(27) = 0
6270 b(c(25)) = 0: c(25) = 0
6250 Next j25
b(c(23)) = 0: c(23) = 0
6230 b(c(20)) = 0: c(20) = 0
6200 b(c(24)) = 0: c(24) = 0
6240 b(c(19)) = 0: c(19) = 0
6190 Next j19
b(c(22)) = 0: c(22) = 0
6220 b(c(18)) = 0: c(18) = 0
6180 Next j18
b(c(21)) = 0: c(21) = 0
6210 b(c(17)) = 0: c(17) = 0
6170 Next j17
6090 b(c(8)) = 0: c(8) = 0
6080 b(c(4)) = 0: c(4) = 0
6040 b(c(7)) = 0: c(7) = 0
6070 b(c(3)) = 0: c(3) = 0
6030 Next j3
b(c(6)) = 0: c(6) = 0
6060 b(c(2)) = 0: c(2) = 0
6020 Next j2
b(c(5)) = 0: c(5) = 0
6050 b(c(1)) = 0: c(1) = 0
6010 Next j1
fl1 = 0
Return
' Determine Magic Square Order 3
2000 fl1 = 1
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)
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(7) = s3 - a(8) - a(9):
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
a(6) = 4 * s3 / 3 - a(8) - 2 * a(9):
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) = s3 / 3:
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50:
''If b1(a(5)) = 0 Then GoTo 50 'will not be used
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(4) = -2 * s3 / 3 + a(8) + 2 * a(9):
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(3) = -s3 / 3 + a(8) + a(9):
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(2) = 2 * s3 / 3 - a(8):
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(1) = 2 * s3 / 3 - a(9):
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
Return
5 b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(2) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(9)) = 0: c(9) = 0
90 Next j9
fl1 = 0
Return
' Determine Main Diagonal and Remaining Pairs
3000 fl1 = 1
' Main Diagonal and Related Border Pairs
For j10 = m1 To m2
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(14) = Pr3 - a(10): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
For j11 = m1 To m2
If b1(a1(j11)) = 0 Then GoTo 110
If b(a1(j11)) = 0 Then b(a1(j11)) = a1(j11): c(11) = a1(j11) Else GoTo 110
a(11) = a1(j11)
a(15) = Pr3 - a(11): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j12 = m1 To m2
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(16) = Pr3 - a(12): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(13) = (s9 - Crnr3(i35)) - a(12) - a(11) - a(10)
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
a(17) = Pr3 - a(13): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(18) = s3 - a(13) - a(16)
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(20) = Pr3 - a(18): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = s3 - a(10) - a(15)
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(21) = Pr3 - a(19): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
' Remaining Magic Rectangles
For j22 = m1 To m2
If b1(a1(j22)) = 0 Then GoTo 220
If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 220
a(22) = a1(j22)
a(25) = Pr3 - a(22): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
For j23 = m1 To m2
If b1(a1(j23)) = 0 Then GoTo 230
If b(a1(j23)) = 0 Then b(a1(j23)) = a1(j23): c(23) = a1(j23) Else GoTo 230
a(23) = a1(j23)
a(26) = Pr3 - a(23): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(24) = s3 - a(22) - a(23)
If a(24) < a1(m1) Or a(24) > a1(m2) Then GoTo 240:
If b1(a(24)) = 0 Then GoTo 240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(27) = Pr3 - a(24): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
For j28 = m1 To m2
If b1(a1(j28)) = 0 Then GoTo 280
If b(a1(j28)) = 0 Then b(a1(j28)) = a1(j28): c(28) = a1(j28) Else GoTo 280
a(28) = a1(j28)
a(31) = Pr3 - a(28): If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
For j29 = m1 To m2
If b1(a1(j29)) = 0 Then GoTo 290
If b(a1(j29)) = 0 Then b(a1(j29)) = a1(j29): c(29) = a1(j29) Else GoTo 290
a(29) = a1(j29)
a(32) = Pr3 - a(29): If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(30) = s3 - a(28) - a(29)
If a(30) < a1(m1) Or a(30) > a1(m2) Then GoTo 300:
If b1(a(30)) = 0 Then GoTo 300
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(33) = Pr3 - a(30): If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
Return
b(c(33)) = 0: c(33) = 0
330 b(c(30)) = 0: c(30) = 0
300 b(c(32)) = 0: c(32) = 0
320 b(c(29)) = 0: c(29) = 0
290 Next j29
b(c(31)) = 0: c(31) = 0
310 b(c(28)) = 0: c(28) = 0
280 Next j28
b(c(27)) = 0: c(27) = 0
270 b(c(24)) = 0: c(24) = 0
240 b(c(26)) = 0: c(26) = 0
260 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(25)) = 0: c(25) = 0
250 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(21)) = 0: c(21) = 0
210 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(18)) = 0: c(18) = 0
180 b(c(17)) = 0: c(17) = 0
170 b(c(13)) = 0: c(13) = 0
130 b(c(16)) = 0: c(16) = 0
160 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(15)) = 0: c(15) = 0
150 b(c(11)) = 0: c(11) = 0
110 Next j11
b(c(14)) = 0: c(14) = 0
140 b(c(10)) = 0: c(10) = 0
100 Next j10
fl1 = 0
Return
' Double Check Identical Numbers a15()
800 fl1 = 1
For i1 = 1 To 225
a20 = a15(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 225
If a20 = a15(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Remove used pairs from b1()
900 For i1 = 1 To n32
b1(a(i1)) = 0
Next i1
Return
' Print results (lines)
1640 Cells(n9, 226).Select
For i1 = 1 To 225
Cells(n9, i1).Value = a15(i1)
Next i1
Cells(n9, 226).Value = s15
Cells(n9, 227).Value = Rcrd1a
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 2 Then
n2 = 1: k1 = k1 + 16: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 16
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = "MC = " + CStr(s15)
i3 = 0
For i1 = 1 To 15
For i2 = 1 To 15
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a15(i3)
Next i2
Next i1
Return
End Sub
