' Generates Simple Magic Squares of order 5, Plus Magic
' Standard Position
' Tested with Office 365 under Windows 10
Sub MgcSqr5d4()
Dim a(25), b(25), c(25), s(12)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr5d4")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 1: m2 = 25: s1 = 65: Pr5 = 26
' Generate data
Sheets("Klad1").Select
t1 = Timer
For j25 = m1 To m2 'a(25)
If b(j25) = 0 Then b(j25) = j25: c(25) = j25 Else GoTo 250
a(25) = j25
For j24 = m1 To m2 'a(24)
If b(j24) = 0 Then b(j24) = j24: c(24) = j24 Else GoTo 240
a(24) = j24
For j23 = m1 To m2 'a(23)
If b(j23) = 0 Then b(j23) = j23: c(23) = j23 Else GoTo 230
a(23) = j23
For j22 = m1 To m2 'a(22)
If b(j22) = 0 Then b(j22) = j22: c(22) = j22 Else GoTo 220
a(22) = j22
a(21) = s1 - a(22) - a(23) - a(24) - a(25)
If a(21) < m1 Or a(21) > m2 Then GoTo 210
If a(21) < a(25) Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
For j20 = m1 To m2 'a(20)
If b(j20) = 0 Then b(j20) = j20: c(20) = j20 Else GoTo 200
a(20) = j20
For j19 = m1 To m2 'a(19)
If b(j19) = 0 Then b(j19) = j19: c(19) = j19 Else GoTo 190
a(19) = j19
a(12) = -s1 + a(19) + a(20) + a(21) + a(23) + a(24) + a(25)
If a(12) < m1 Or a(12) > m2 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j18 = m1 To m2 'a(18)
If b(j18) = 0 Then b(j18) = j18: c(18) = j18 Else GoTo 180
a(18) = j18
a(14) = s1 - a(18) - a(19) - a(20) - a(24)
If a(14) < m1 Or a(14) > m2 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(3) = -a(18) + a(21) + a(25)
If a(3) < m1 Or a(3) > m2 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j17 = m1 To m2 'a(17)
If b(j17) = 0 Then b(j17) = j17: c(17) = j17 Else GoTo 170
a(17) = j17
a(16) = s1 - a(17) - a(18) - a(19) - a(20)
If a(16) < m1 Or a(16) > m2 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
For j15 = m1 To m2 'a(15)
If b(j15) = 0 Then b(j15) = j15: c(15) = j15 Else GoTo 150
a(15) = j15
a(9) = a(15) - a(17) + a(19) + a(20) - a(21) - a(22) + a(25)
If a(9) < m1 Or a(9) > m2 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(4) = s1 - a(15) + a(17) + a(18) - a(19) - a(23) - a(24) - 2 * a(25)
If a(4) < m1 Or a(4) > m2 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(1) = -s1 + a(15) + a(19) + a(20) + a(23) + a(24) + a(25)
If a(1) < m1 Or a(1) > m2 Then GoTo 10
If a(1) < a(25) Then GoTo 10
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j13 = m1 To m2 'a(13)
If b(j13) = 0 Then b(j13) = j13: c(13) = j13 Else GoTo 130
a(13) = j13
a(11) = s1 - a(13) - a(15) + a(18) - a(21) - a(23) - a(25)
If a(11) < m1 Or a(11) > m2 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(10) = a(13) + a(19) - a(22)
If a(10) < m1 Or a(10) > m2 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(8) = s1 - a(13) - a(21) - a(23) - a(25)
If a(8) < m1 Or a(8) > m2 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(7) = 2 * s1 - a(13) - a(15) - 2 * a(19) - a(20) - a(23) - a(24) - 2 * a(25)
If a(7) < m1 Or a(7) > m2 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = a(13) + a(17) - a(24)
If a(6) < m1 Or a(6) > m2 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = s1 - a(13) - a(15) - a(19) - a(20) + a(22) - a(25)
If a(5) < m1 Or a(5) > m2 Then GoTo 50
If a(5) < a(25) Then GoTo 50
If a(5) < a(21) Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(2) = a(13) + a(15) - a(17) + a(19) - a(21) - a(22) + a(25)
If a(2) < m1 Or a(2) > m2 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
' Prevent Pan Magic or Associated Squares
GoSub 500: If fl1 = 0 Then GoTo 5
n9 = n9 + 1
GoSub 650 'Print results (squares)
' GoSub 640 'Print results (selected numbers)
' Cells(1, 1).Value = n9 'Counting
5
b(c(2)) = 0: c(2) = 0
20 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 b(c(10)) = 0: c(10) = 0
100 b(c(11)) = 0: c(11) = 0
110 b(c(13)) = 0: c(13) = 0
130 Next j13
b(c(1)) = 0: c(1) = 0
10 b(c(4)) = 0: c(4) = 0
40 b(c(9)) = 0: c(9) = 0
90 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(16)) = 0: c(16) = 0
160 b(c(17)) = 0: c(17) = 0
170 Next j17
b(c(3)) = 0: c(3) = 0
30 b(c(14)) = 0: c(14) = 0
140 b(c(18)) = 0: c(18) = 0
180 Next j18
b(c(12)) = 0: c(12) = 0
120 b(c(19)) = 0: c(19) = 0
190 Next j19
b(c(20)) = 0: c(20) = 0
200 Next j20
b(c(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(25)) = 0: c(25) = 0
250 Next j25
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqr5d4")
End
' Prevent Pan Magic or Associated Squares
500 fl1 = 1
' Broken Diagonals
s(1) = a(2) + a(8) + a(14) + a(20) + a(21)
s(2) = a(3) + a(9) + a(15) + a(16) + a(22)
s(3) = a(4) + a(10) + a(11) + a(17) + a(23)
s(4) = a(5) + a(6) + a(12) + a(18) + a(24)
s(5) = a(4) + a(8) + a(12) + a(16) + a(25)
s(6) = a(3) + a(7) + a(11) + a(20) + a(24)
s(7) = a(2) + a(6) + a(15) + a(19) + a(23)
s(8) = a(1) + a(10) + a(14) + a(18) + a(22)
n5 = 0
For i1 = 1 To 8
If s(i1) = s1 Then n5 = n5 + 1
Next i1
If n5 = 8 Then fl1 = 0: Return
' Associated Pairs
s(1) = a(1) + a(25): s(2) = a(2) + a(24): s(3) = a(3) + a(23): s(4) = a(4) + a(22):
s(5) = a(5) + a(21): s(6) = a(6) + a(20): s(7) = a(7) + a(19): s(8) = a(8) + a(18):
s(9) = a(9) + a(17): s(10) = a(10) + a(16): s(11) = a(11) + a(15): s(12) = a(12) + a(14):
n5 = 0
For i1 = 1 To 12
If s(i1) = Pr5 Then n5 = n5 + 1
Next i1
If n5 = 12 Then fl1 = 0: Return
Return
' Print results (selected numbers)
640 For i1 = 1 To 25
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 6: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 6
End If
Cells(1, 1).Value = n9
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
i3 = 0
For i1 = 1 To 5
For i2 = 1 To 5
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
