' Generates order 5 Crosswise Symmetric Magic Squares of Subtraction, Res5 = 13
' Tested with Office 365 under Windows 10
Sub SubtrSqr5c()
Dim a1(25), a(25), b1(25), b(25), c(25)
Dim b5(5), Res5(12), s(10)
y = MsgBox("Locked", vbCritical, "Routine SubtrSqr5c")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
Sheets("Klad1").Select
t1 = Timer
' Define variables
GoSub 2010 'Natural Numbers
a(13) = Pr5 / 2: b(a(13)) = a(13) 'Fix Center
For j25 = m1 To m2 'a(25)
If b(a1(j25)) = 0 Then b(a1(j25)) = a1(j25): c(25) = a1(j25) Else GoTo 250
a(25) = a1(j25)
a(19) = Pr5 - a(25): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
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(20) = Pr5 - a(24): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
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(18) = Pr5 - a(23): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
For j22 = m1 To m2 '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(16) = Pr5 - a(22): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
For j21 = j25 To m2 'a(21) Unique
If b(a1(j21)) = 0 Then b(a1(j21)) = a1(j21): c(21) = a1(j21) Else GoTo 210
a(21) = a1(j21)
a(17) = Pr5 - a(21): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
i10 = 5: GoSub 1000: If Res5(i10) <> r5 Then GoTo 165
For j15 = m1 To m2 'a(15)
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(14) = Pr5 - a(15): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
For j12 = m1 To m2 'a(12)
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(11) = Pr5 - a(12): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
i10 = 3: GoSub 1000: If Res5(i10) <> r5 Then GoTo 105
For j10 = m1 To m2 'a(10)
If b(a1(j10)) = 0 Then b(a1(j10)) = a1(j10): c(10) = a1(j10) Else GoTo 100
a(10) = a1(j10)
a(4) = Pr5 - a(10): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j9 = m1 To m2 'a(9)
If b(a1(j9)) = 0 Then b(a1(j9)) = a1(j9): c(9) = a1(j9) Else GoTo 90
a(9) = a1(j9)
a(5) = Pr5 - a(9):
If a(5) < a(25) Then GoTo 50 'Unique
If a(5) < a(21) Then GoTo 50 'Unique
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j8 = m1 To m2 'a(8)
If b(a1(j8)) = 0 Then b(a1(j8)) = a1(j8): c(8) = a1(j8) Else GoTo 80
a(8) = a1(j8)
a(3) = Pr5 - a(8): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j7 = m1 To m2 'a(7)
If b(a1(j7)) = 0 Then b(a1(j7)) = a1(j7): c(7) = a1(j7) Else GoTo 70
a(7) = a1(j7)
a(1) = Pr5 - a(7):
If a(1) < a(25) Then GoTo 10 'Unique
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j6 = m1 To m2 'a(6)
If b(a1(j6)) = 0 Then b(a1(j6)) = a1(j6): c(6) = a1(j6) Else GoTo 60
a(6) = a1(j6)
a(2) = Pr5 - a(6): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
' Check Remainder and Back Check
For i10 = 1 To 12
GoSub 1000: If Res5(i10) <> r5 Then GoTo 5
Next i10
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
n10 = n10 + 1
n9 = n9 + 1: GoSub 650 'Print results (squares)
' n9 = n9 + 1: GoSub 640 'Print results (selected numbers)
' n9 = n9 + 1: Cells(1, 1).Value = n9
5
b(c(2)) = 0: c(2) = 0
20 b(c(6)) = 0: c(6) = 0
60 Next j6
b(c(1)) = 0: c(1) = 0
10 b(c(7)) = 0: c(7) = 0
70 Next j7
b(c(3)) = 0: c(3) = 0
30 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(5)) = 0: c(5) = 0
50 b(c(9)) = 0: c(9) = 0
90 Next j9
b(c(4)) = 0: c(4) = 0
40 b(c(10)) = 0: c(10) = 0
100 Next j10
105 b(c(11)) = 0: c(11) = 0
110 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
150 Next j15
165 b(c(17)) = 0: c(17) = 0
170 b(c(21)) = 0: c(21) = 0
210 Next j21
b(c(16)) = 0: c(16) = 0
160 b(c(22)) = 0: c(22) = 0
220 Next j22
b(c(18)) = 0: c(18) = 0
180 b(c(23)) = 0: c(23) = 0
230 Next j23
b(c(20)) = 0: c(20) = 0
200 b(c(24)) = 0: c(24) = 0
240 Next j24
b(c(19)) = 0: c(19) = 0
190 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 SubtrSqr5c")
End
' Define Variables (Natural Numbers)
2010
m1 = 1: m2 = 25
For i1 = 1 To 25
a1(i1) = i1: b1(i1) = i1
Next i1
s1 = 65: r5 = 13
Pr5 = 26
Return
' Print results (selected numbers)
640 Cells(n9, 25).Select
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(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
Cells(k1, k2 + 2).Value = r5
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
' Exclude solutions with identical numbers or out of range
800 fl1 = 1
For j1 = 1 To 25
a2 = a(j1): If a2 = 0 Then GoTo 810
For j2 = (1 + j1) To 25
If a2 = a(j2) Then fl1 = 0: Return
Next j2
810 Next j1
Return
' determine Residuum line i10
1000
Select Case i10
' Rows
Case 1:
b5(1) = a(1): b5(2) = a(2): b5(3) = a(3): b5(4) = a(4): b5(5) = a(5):
GoSub 1200
Case 2:
b5(1) = a(6): b5(2) = a(7): b5(3) = a(8): b5(4) = a(9):: b5(5) = a(10):
GoSub 1200
Case 3:
b5(1) = a(11): b5(2) = a(12): b5(3) = a(13): b5(4) = a(14):: b5(5) = a(15):
GoSub 1200
Case 4:
b5(1) = a(16): b5(2) = a(17): b5(3) = a(18): b5(4) = a(19):: b5(5) = a(20):
GoSub 1200
Case 5:
b5(1) = a(21): b5(2) = a(22): b5(3) = a(23): b5(4) = a(24):: b5(5) = a(25):
GoSub 1200
' Columns
Case 6:
b5(1) = a(1): b5(2) = a(6): b5(3) = a(11): b5(4) = a(16):: b5(5) = a(21):
GoSub 1200
Case 7:
b5(1) = a(2): b5(2) = a(7): b5(3) = a(12): b5(4) = a(17):: b5(5) = a(22):
GoSub 1200
Case 8:
b5(1) = a(3): b5(2) = a(8): b5(3) = a(13): b5(4) = a(18):: b5(5) = a(23):
GoSub 1200
Case 9:
b5(1) = a(4): b5(2) = a(9): b5(3) = a(14): b5(4) = a(19):: b5(5) = a(24):
GoSub 1200
Case 10:
b5(1) = a(5): b5(2) = a(10): b5(3) = a(15): b5(4) = a(20):: b5(5) = a(25):
GoSub 1200
' Diagonals
Case 11:
b5(1) = a(1): b5(2) = a(7): b5(3) = a(13): b5(4) = a(19):: b5(5) = a(25):
GoSub 1200
Case 12:
b5(1) = a(5): b5(2) = a(9): b5(3) = a(13): b5(4) = a(17):: b5(5) = a(21):
GoSub 1200
End Select
Return
1200
For i2 = 1 To 4
For i1 = i2 To 5
If b5(i2) < b5(i1) Then
x = b5(i1)
b5(i1) = b5(i2)
b5(i2) = x
End If
Next i1
Next i2
Res5(i10) = b5(1) - b5(2) + b5(3) - b5(4) + b5(5)
Return
End Sub
