' Generates Associated Bimagic Squares of order 6
' Tested with Office 2007 under Windows 7
Sub MagSqrs62e()
Dim a(36), b(135), c(36), a1(6), a2(6), a3(36), b1(135), s(14)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr62e")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
ShtNm1 = "BlncdLns62"
Sheets("Klad1").Select
t1 = Timer
GoSub 2000 'Predefined Integers
' GoSub 2010 'Full Range
For j100 = 3 To 4
' Read Sets Bimagic Series (Preselected)
For i1 = 1 To 6
a1(i1) = Sheets(ShtNm1).Cells(j100, i1).Value
Next i1
For i1 = 1 To 6
a2(i1) = Sheets(ShtNm1).Cells(j100, i1 + 6).Value
Next i1
' Diagonal Rbtm/Ltop
For j36 = 1 To 6 'a(36)
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 315
a(36) = a1(j36)
a(1) = Pr6 - a(36): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j29 = 1 To 6 'a(29)
If b(a1(j29)) = 0 Then b(a1(j29)) = a1(j29): c(29) = a1(j29) Else GoTo 290
a(29) = a1(j29)
a(8) = Pr6 - a(29): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j22 = 1 To 6 'a(22)
If b(a1(j22)) = 0 Then b(a1(j22)) = a1(j22): c(22) = a1(j22) Else GoTo 220
a(22) = a1(j22)
a(15) = Pr6 - a(22): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
' Diagonal Lbtm/Rtop
For j31 = 1 To 6 'a(31)
If b(a2(j31)) = 0 Then b(a2(j31)) = a2(j31): c(31) = a2(j31) Else GoTo 316
a(31) = a2(j31)
a(6) = Pr6 - a(31): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j26 = 1 To 6 'a(26)
If b(a2(j26)) = 0 Then b(a2(j26)) = a2(j26): c(26) = a2(j26) Else GoTo 260
a(26) = a2(j26)
a(11) = Pr6 - a(26): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j21 = 1 To 6 'a(21)
If b(a2(j21)) = 0 Then b(a2(j21)) = a2(j21): c(21) = a2(j21) Else GoTo 210
a(21) = a2(j21)
a(16) = Pr6 - a(21): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
'Row 1/6
For j35 = m1 To m2 'a(35)
If b(a3(j35)) = 0 Then b(a3(j35)) = a3(j35): c(35) = a3(j35) Else GoTo 350
a(35) = a3(j35)
a(2) = Pr6 - a(35): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j34 = m1 To m2 'a(34)
If b(a3(j34)) = 0 Then b(a3(j34)) = a3(j34): c(34) = a3(j34) Else GoTo 340
a(34) = a3(j34)
a(3) = Pr6 - a(34): 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(a3(j33)) = 0 Then b(a3(j33)) = a3(j33): c(33) = a3(j33) Else GoTo 330
a(33) = a3(j33)
a(4) = Pr6 - a(33): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(32) = s1 - a(31) - a(33) - a(34) - a(35) - a(36)
If a(32) < a3(m1) Or a(32) > a3(m2) Then GoTo 320
If b1(a(32)) = 0 Then GoTo 320
If b(a(32)) = 0 Then b(a(32)) = a(32): c(32) = a(32) Else GoTo 320
a(5) = Pr6 - a(32): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
s22 = a(31) ^ 2 + a(32) ^ 2 + a(33) ^ 2 + a(34) ^ 2 + a(35) ^ 2 + a(36) ^ 2
If s22 <> s2 Then GoTo 55
'Column 2/5
For j23 = m1 To m2 'a(23)
If b(a3(j23)) = 0 Then b(a3(j23)) = a3(j23): c(23) = a3(j23) Else GoTo 230
a(23) = a3(j23)
a(14) = Pr6 - a(23): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(17) = s1 - a(5) - a(11) - a(23) - a(29) - a(35)
If a(17) < a3(m1) Or a(17) > a3(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(20) = Pr6 - a(17): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
s22 = a(5) ^ 2 + a(11) ^ 2 + a(17) ^ 2 + a(23) ^ 2 + a(29) ^ 2 + a(35) ^ 2
If s22 <> s2 Then GoTo 205
'Column 3/4
For j28 = m1 To m2 'a(28)
If b(a3(j28)) = 0 Then b(a3(j28)) = a3(j28): c(28) = a3(j28) Else GoTo 280
a(28) = a3(j28)
a(9) = Pr6 - a(28): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(10) = s1 - a(4) - a(16) - a(22) - a(28) - a(34)
If a(10) < a3(m1) Or a(10) > a3(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(27) = Pr6 - a(10): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
s22 = a(4) ^ 2 + a(10) ^ 2 + a(16) ^ 2 + a(22) ^ 2 + a(28) ^ 2 + a(34) ^ 2
If s22 <> s2 Then GoTo 275
'Row 3/4
For j24 = m1 To m2 'a(24)
If b(a3(j24)) = 0 Then b(a3(j24)) = a3(j24): c(24) = a3(j24) Else GoTo 240
a(24) = a3(j24)
a(13) = Pr6 - a(24): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(19) = s1 - a(20) - a(21) - a(22) - a(23) - a(24)
If a(19) < a3(m1) Or a(19) > a3(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) = Pr6 - a(19): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
s22 = a(19) ^ 2 + a(20) ^ 2 + a(21) ^ 2 + a(22) ^ 2 + a(23) ^ 2 + a(24) ^ 2
If s22 <> s2 Then GoTo 185
'Remainder
a(12) = 4*s1/6 - a(24) + a(28) - a(23) - a(33) - a(21) + a(26) + (a(2)-a(35)-a(8)-a(29)+a(1)-a(36))/2
If a(12) < a3(m1) Or a(12) > a3(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(25) = Pr6 - a(12): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(30) = s1 - a(6) - a(12) - a(18) - a(24) - a(36)
If a(30) < a3(m1) Or a(30) > a3(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(7) = Pr6 - a(30): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 300
s22 = a(6) ^ 2 + a(12) ^ 2 + a(18) ^ 2 + a(24) ^ 2 + a(30) ^ 2 + a(36) ^ 2
If s22 <> s2 Then GoTo 5
GoSub 800: If fl1 = 0 Then GoTo 5 ' Back Check Identical Numbers
GoSub 900: If fl1 = 0 Then GoTo 5 ' Back Check Bimagic
n9 = n9 + 1: GoSub 650 'Print results (squares)
' n9 = n9 + 1: GoSub 645 'Print results (selected numbers)
' Erase b, c: GoTo 1000 'Print only first square (Option)
5
b(c(7)) = 0: c(7) = 0
70 b(c(30)) = 0: c(30) = 0
300 b(c(25)) = 0: c(25) = 0
250 b(c(12)) = 0: c(12) = 0
120
185
b(c(18)) = 0: c(18) = 0
180 b(c(19)) = 0: c(19) = 0
190 b(c(13)) = 0: c(13) = 0
130 b(c(24)) = 0: c(24) = 0
240 Next j24
275
b(c(27)) = 0: c(27) = 0
270 b(c(10)) = 0: c(10) = 0
100 b(c(9)) = 0: c(9) = 0
90 b(c(28)) = 0: c(28) = 0
280 Next j28
205
b(c(20)) = 0: c(20) = 0
200 b(c(17)) = 0: c(17) = 0
170 b(c(14)) = 0: c(14) = 0
140 b(c(23)) = 0: c(23) = 0
230 Next j23
55
b(c(5)) = 0: c(5) = 0
50 b(c(32)) = 0: c(32) = 0
320 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(2)) = 0: c(2) = 0
20 b(c(35)) = 0: c(35) = 0
350 Next j35
b(c(16)) = 0: c(16) = 0
160 b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(11)) = 0: c(11) = 0
110 b(c(26)) = 0: c(26) = 0
260 Next j26
b(c(6)) = 0: c(6) = 0
60 b(c(31)) = 0: c(31) = 0
316 Next j31
b(c(15)) = 0: c(15) = 0
150 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(8)) = 0: c(8) = 0
80 b(c(29)) = 0: c(29) = 0
290 Next j29
b(c(1)) = 0: c(1) = 0
10 b(c(36)) = 0: c(36) = 0
315 Next j36
1000 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqr62e")
End
' Exclude solutions with identical numbers
800 fl1 = 1
For i1 = 1 To 36
a20 = a(i1): If a20 = 0 Then GoTo 810
For i2 = (1 + i1) To 36
If a20 = a(i2) Then fl1 = 0: Return
Next i2
810 Next i1
Return
' Back Check Bimagic
900 fl1 = 1
s(1) = a(1) ^ 2 + a(2) ^ 2 + a(3) ^ 2 + a(4) ^ 2 + a(5) ^ 2 + a(6) ^ 2
s(2) = a(7) ^ 2 + a(8) ^ 2 + a(9) ^ 2 + a(10) ^ 2 + a(11) ^ 2 + a(12) ^ 2
s(3) = a(13) ^ 2 + a(14) ^ 2 + a(15) ^ 2 + a(16) ^ 2 + a(17) ^ 2 + a(18) ^ 2
s(4) = a(19) ^ 2 + a(20) ^ 2 + a(21) ^ 2 + a(22) ^ 2 + a(23) ^ 2 + a(24) ^ 2
s(5) = a(25) ^ 2 + a(26) ^ 2 + a(27) ^ 2 + a(28) ^ 2 + a(29) ^ 2 + a(30) ^ 2
s(6) = a(31) ^ 2 + a(32) ^ 2 + a(33) ^ 2 + a(34) ^ 2 + a(35) ^ 2 + a(36) ^ 2
s(7) = a(1) ^ 2 + a(7) ^ 2 + a(13) ^ 2 + a(19) ^ 2 + a(25) ^ 2 + a(31) ^ 2
s(8) = a(2) ^ 2 + a(8) ^ 2 + a(14) ^ 2 + a(20) ^ 2 + a(26) ^ 2 + a(32) ^ 2
s(9) = a(3) ^ 2 + a(9) ^ 2 + a(15) ^ 2 + a(21) ^ 2 + a(27) ^ 2 + a(33) ^ 2
s(10) = a(4) ^ 2 + a(10) ^ 2 + a(16) ^ 2 + a(22) ^ 2 + a(28) ^ 2 + a(34) ^ 2
s(11) = a(5) ^ 2 + a(11) ^ 2 + a(17) ^ 2 + a(23) ^ 2 + a(29) ^ 2 + a(35) ^ 2
s(12) = a(6) ^ 2 + a(12) ^ 2 + a(18) ^ 2 + a(24) ^ 2 + a(30) ^ 2 + a(36) ^ 2
s(13) = a(1) ^ 2 + a(8) ^ 2 + a(15) ^ 2 + a(22) ^ 2 + a(29) ^ 2 + a(36) ^ 2
s(14) = a(6) ^ 2 + a(11) ^ 2 + a(16) ^ 2 + a(21) ^ 2 + a(26) ^ 2 + a(31) ^ 2
' Check Bimagic
For j20 = 1 To 14
If s(j20) <> s2 Then fl1 = 0: Return
Next j20
Return
' Print results (selected numbers)
645 For i1 = 1 To 36
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 37).Value = j100
Cells(n9, 38).Value = n9
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 7: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 7
End If
Cells(k1, k2 + 1).Select
Range(Cells(k1, k2 + 1), Cells(k1, k2 + 4)).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
i3 = 0
For i1 = 1 To 6
For i2 = 1 To 6
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Predefined Integers
2000 m1 = 1: m2 = 36:
s1 = 408: s2 = 36826: Pr6 = s1 / 3
a3(1) = 1: a3(2) = 7: a3(3) = 12: a3(4) = 17: a3(5) = 20: a3(6) = 22:
a3(7) = 25: a3(8) = 28: a3(9) = 34: a3(10) = 36: a3(11) = 38: a3(12) = 40:
a3(13) = 44: a3(14) = 49: a3(15) = 50: a3(16) = 55: a3(17) = 58: a3(18) = 62:
a3(19) = 74: a3(20) = 78: a3(21) = 81: a3(22) = 86: a3(23) = 87: a3(24) = 92:
a3(25) = 96: a3(26) = 98: a3(27) = 100: a3(28) = 102: a3(29) = 108: a3(30) = 111:
a3(31) = 114: a3(32) = 116: a3(33) = 119: a3(34) = 124: a3(35) = 129: a3(36) = 135:
Erase b1
For i1 = m1 To m2
b1(a3(i1)) = a3(i1)
Next i1
Return
' Full Range
2010 m1 = 1: m2 = 135:
s1 = 408: s2 = 36826: Pr6 = s1 / 3
Erase b1
For i1 = 1 To m2
a3(i1) = i1: b1(i1) = i1
Next i1
Return
End Sub
