' Generates order 7 Associated Magic Squares of Subtraction (s7 = 175, Res7 = 25)
' Overlapping Sub Squares (s4 = 100)
' Tested with Office 365 under Windows 10
Sub OverlSqrs7()
Dim a1(49), a(49), b1(49), b(49), c(49)
Dim b7(7), Res7(16)
y = MsgBox("Locked", vbCritical, "Routine OverlSqrs7")
End
n2 = 0: n3 = 0: n9 = 0: k1 = 1: k2 = 1
Sheets("Klad1").Select
t1 = Timer
' Define variables
GoSub 2000 ' Read Natural Numbers
a(25) = s1 / 7: b(a(25)) = a(25)
For j26 = m1 To m2 'a(26)
If b(a1(j26)) = 0 Then b(a1(j26)) = a1(j26): c(26) = a1(j26) Else GoTo 260
a(26) = a1(j26)
a(24) = Pr7 - a(26): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
For j27 = m1 To m2 'a(27)
If b(a1(j27)) = 0 Then b(a1(j27)) = a1(j27): c(27) = a1(j27) Else GoTo 270
a(27) = a1(j27)
a(28) = 4 * s1 / 7 - a(25) - a(26) - a(27)
If a(28) < a1(m1) Or a(28) > a1(m2) Then GoTo 280
If b1(a(28)) = 0 Then GoTo 280
If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(23) = Pr7 - a(27): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = Pr7 - a(28): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
For j32 = m1 To m2 'a(32)
If b(a1(j32)) = 0 Then b(a1(j32)) = a1(j32): c(32) = a1(j32) Else GoTo 320
a(32) = a1(j32)
a(18) = Pr7 - a(32): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
For j33 = m1 To m2 'a(33)
If b(a1(j33)) = 0 Then b(a1(j33)) = a1(j33): c(33) = a1(j33) Else GoTo 330
a(33) = a1(j33)
a(17) = Pr7 - a(33): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
For j34 = m1 To m2 'a(34)
If b(a1(j34)) = 0 Then b(a1(j34)) = a1(j34): c(34) = a1(j34) Else GoTo 340
a(34) = a1(j34)
a(35) = 4 * s1 / 7 - a(32) - a(33) - a(34)
If a(35) < a1(m1) Or a(35) > a1(m2) Then GoTo 350
If b1(a(35)) = 0 Then GoTo 350
If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(16) = Pr7 - a(34): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(15) = Pr7 - a(35): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j39 = m1 To m2 'a(39)
If b(a1(j39)) = 0 Then b(a1(j39)) = a1(j39): c(39) = a1(j39) Else GoTo 390
a(39) = a1(j39)
a(40) = a(39) - a(34) + a(32) - a(28) + a(25)
If a(40) < a1(m1) Or a(40) > a1(m2) Then GoTo 400
If b1(a(40)) = 0 Then GoTo 400
If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(41) = 4 * s1 / 7 - a(39) - a(33) - a(32) + a(28) - a(25)
If a(41) < a1(m1) Or a(41) > a1(m2) Then GoTo 410
If b1(a(41)) = 0 Then GoTo 410
If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(42) = -a(39) + a(34) + a(33)
If a(42) < a1(m1) Or a(42) > a1(m2) Then GoTo 420
If b1(a(42)) = 0 Then GoTo 420
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(46) = 4 * s1 / 7 - a(40) - a(34) - a(28)
If a(46) < a1(m1) Or a(46) > a1(m2) Then GoTo 460
If b1(a(46)) = 0 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(47) = -4 * s1 / 7 - a(39) + a(35) + 2 * a(34) + 2 * a(28) + a(27)
If a(47) < a1(m1) Or a(47) > a1(m2) Then GoTo 470
If b1(a(47)) = 0 Then GoTo 470
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(48) = a(39) - a(35) - 2 * a(34) + a(26) + 2 * a(25)
If a(48) < a1(m1) Or a(48) > a1(m2) Then GoTo 480
If b1(a(48)) = 0 Then GoTo 480
If b(a(48)) = 0 Then b(a(48)) = a(48): c(48) = a(48) Else GoTo 480
a(49) = a(39) + a(32) - a(28)
If a(49) < a1(m1) Or a(49) > a1(m2) Then GoTo 490
If b1(a(49)) = 0 Then GoTo 490
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
a(11) = Pr7 - a(39): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(10) = Pr7 - a(40): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(9) = Pr7 - a(41): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
a(8) = Pr7 - a(42): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(4) = Pr7 - a(46): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(3) = Pr7 - a(47): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = Pr7 - a(48): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = Pr7 - a(49): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j45 = m1 To m2 'a(45)
If b(a1(j45)) = 0 Then b(a1(j45)) = a1(j45): c(45) = a1(j45) Else GoTo 450
a(45) = a1(j45)
a(5) = Pr7 - a(45): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j44 = m1 To m2 'a(44)
If b(a1(j44)) = 0 Then b(a1(j44)) = a1(j44): c(44) = a1(j44) Else GoTo 440
a(44) = a1(j44)
a(43) = 3 * s1 / 7 - a(44) - a(45)
If a(43) < a1(m1) Or a(43) > a1(m2) Then GoTo 430
If b1(a(43)) = 0 Then GoTo 430
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(7) = Pr7 - a(43): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = Pr7 - a(44): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
i10 = 7: GoSub 1000: If Res7(i10) <> 25 Then GoTo 55
For j38 = m1 To m2 'a(38)
If b(a1(j38)) = 0 Then b(a1(j38)) = a1(j38): c(38) = a1(j38) Else GoTo 380
a(38) = a1(j38)
a(31) = 3 * s1 / 7 - a(38) - a(45)
If a(31) < a1(m1) Or a(31) > a1(m2) Then GoTo 310
If b1(a(31)) = 0 Then GoTo 310
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(19) = Pr7 - a(31): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(12) = Pr7 - a(38): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j37 = m1 To m2 'a(37)
If b(a1(j37)) = 0 Then b(a1(j37)) = a1(j37): c(37) = a1(j37) Else GoTo 370
a(37) = a1(j37)
a(36) = 3 * s1 / 7 - a(37) - a(38)
If a(36) < a1(m1) Or a(36) > a1(m2) Then GoTo 360
If b1(a(36)) = 0 Then GoTo 360
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
i10 = 6: GoSub 1000: If Res7(i10) <> 25 Then GoTo 355
i10 = 10: GoSub 1000: If Res7(i10) <> 25 Then GoTo 355
a(30) = 3 * s1 / 7 - a(37) - a(44)
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(29) = -3 * s1 / 7 + a(37) + a(38) + a(44) + a(45)
If a(29) < a1(m1) Or a(29) > a1(m2) Then GoTo 290
If b1(a(29)) = 0 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(21) = Pr7 - a(29): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = Pr7 - a(30): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(14) = Pr7 - a(36): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = Pr7 - a(37): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
i10 = 5: GoSub 1000: If Res7(i10) <> 25 Then GoTo 5
i10 = 8: GoSub 1000: If Res7(i10) <> 25 Then GoTo 5
i10 = 9: GoSub 1000: If Res7(i10) <> 25 Then GoTo 5
' Exclude solutions with identical numbers (Back Check)
GoSub 800: If fl1 = 0 Then GoTo 5
n9 = n9 + 1
GoSub 2650 'Print results (squares)
' GoSub 2645 'Print results (selected numbers)
' Erase b, c: GoTo 260 'Print only first square for j26
5
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(20)) = 0: c(20) = 0
200 b(c(21)) = 0: c(21) = 0
210 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300
355 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 Next j37
b(c(12)) = 0: c(12) = 0
120 b(c(19)) = 0: c(19) = 0
190 b(c(31)) = 0: c(31) = 0
310 b(c(38)) = 0: c(38) = 0
380 Next j38
55 b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 Next j44
b(c(5)) = 0: c(5) = 0
50 b(c(45)) = 0: c(45) = 0
450 Next j45
b(c(1)) = 0: c(1) = 0
10 b(c(2)) = 0: c(2) = 0
20 b(c(3)) = 0: c(3) = 0
30 b(c(4)) = 0: c(4) = 0
40 b(c(8)) = 0: c(8) = 0
80 b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 b(c(11)) = 0: c(11) = 0
110 b(c(49)) = 0: c(49) = 0
490 b(c(48)) = 0: c(48) = 0
480 b(c(47)) = 0: c(47) = 0
470 b(c(46)) = 0: c(46) = 0
460 b(c(42)) = 0: c(42) = 0
420 b(c(41)) = 0: c(41) = 0
410 b(c(40)) = 0: c(40) = 0
400 b(c(39)) = 0: c(39) = 0
390 Next j39
b(c(15)) = 0: c(15) = 0
150 b(c(16)) = 0: c(16) = 0
160 b(c(35)) = 0: c(35) = 0
350 b(c(34)) = 0: c(34) = 0
340 Next j34
b(c(17)) = 0: c(17) = 0
170 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(18)) = 0: c(18) = 0
180 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 b(c(28)) = 0: c(28) = 0
280 b(c(27)) = 0: c(27) = 0
270 Next j27
b(c(24)) = 0: c(24) = 0
240 b(c(26)) = 0: c(26) = 0
260 Next j26
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine OverlSqrs7")
End
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 49
a2 = a(j1)
For j2 = (1 + j1) To 49
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Print results (selected numbers)
2645 For i1 = 1 To 49
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 8: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 8
End If
Cells(k1 + 1, k2 + 1).Select
'' Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
i3 = 0
For i1 = 1 To 7
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Read Natural Numbers
2000 m1 = 1: m2 = 49: s1 = 175: Pr7 = 50
For i1 = m1 To m2
a1(i1) = i1
Next i1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
Return
' determine Residuum line i10
1000
Select Case i10
' Rows
Case 1:
b7(1) = a(1): b7(2) = a(2): b7(3) = a(3): b7(4) = a(4): b7(5) = a(5): b7(6) = a(6): b7(7) = a(7):
GoSub 1200
Case 2:
b7(1) = a(8): b7(2) = a(9): b7(3) = a(10): b7(4) = a(11): b7(5) = a(12): b7(6) = a(13): b7(7) = a(14):
GoSub 1200
Case 3:
b7(1) = a(15): b7(2) = a(16): b7(3) = a(17): b7(4) = a(18): b7(5) = a(19): b7(6) = a(20): b7(7) = a(21):
GoSub 1200
Case 4:
b7(1) = a(22): b7(2) = a(23): b7(3) = a(24): b7(4) = a(25): b7(5) = a(26): b7(6) = a(27): b7(7) = a(28):
GoSub 1200
Case 5:
b7(1) = a(29): b7(2) = a(30): b7(3) = a(31): b7(4) = a(32): b7(5) = a(33): b7(6) = a(34): b7(7) = a(35):
GoSub 1200
Case 6:
b7(1) = a(36): b7(2) = a(37): b7(3) = a(38): b7(4) = a(39): b7(5) = a(40): b7(6) = a(41): b7(7) = a(42):
GoSub 1200
Case 7:
b7(1) = a(43): b7(2) = a(44): b7(3) = a(45): b7(4) = a(46): b7(5) = a(47): b7(6) = a(48): b7(7) = a(49):
GoSub 1200
' Columns
Case 8:
b7(1) = a(1): b7(2) = a(8): b7(3) = a(15): b7(4) = a(22): b7(5) = a(29): b7(6) = a(36): b7(7) = a(43):
GoSub 1200
Case 9:
b7(1) = a(2): b7(2) = a(9): b7(3) = a(16): b7(4) = a(23): b7(5) = a(30): b7(6) = a(37): b7(7) = a(44):
GoSub 1200
Case 10:
b7(1) = a(3): b7(2) = a(10): b7(3) = a(17): b7(4) = a(24): b7(5) = a(31): b7(6) = a(38): b7(7) = a(45):
GoSub 1200
Case 11:
b7(1) = a(4): b7(2) = a(11): b7(3) = a(18): b7(4) = a(25): b7(5) = a(32): b7(6) = a(39): b7(7) = a(46):
GoSub 1200
Case 12:
b7(1) = a(5): b7(2) = a(12): b7(3) = a(19): b7(4) = a(26): b7(5) = a(33): b7(6) = a(40): b7(7) = a(47):
GoSub 1200
Case 13:
b7(1) = a(6): b7(2) = a(13): b7(3) = a(20): b7(4) = a(27): b7(5) = a(34): b7(6) = a(41): b7(7) = a(48):
GoSub 1200
Case 14:
b7(1) = a(7): b7(2) = a(14): b7(3) = a(21): b7(4) = a(28): b7(5) = a(35): b7(6) = a(42): b7(7) = a(49):
GoSub 1200
' Diagonals
Case 15:
b7(1) = a(1): b7(2) = a(9): b7(3) = a(17): b7(4) = a(25): b7(5) = a(33): b7(6) = a(41): b7(7) = a(49):
GoSub 1200
Case 16:
b7(1) = a(7): b7(2) = a(13): b7(3) = a(19): b7(4) = a(25): b7(5) = a(31): b7(6) = a(37): b7(7) = a(43):
GoSub 1200
End Select
Return
' check n25
1050
n25 = 0
For i1 = 1 To 16
If Res7(i1) = 25 Then n25 = n25 + 1
Next i1
Return
1200
For i2 = 1 To 6
For i1 = i2 To 7
If b7(i2) < b7(i1) Then
x = b7(i1)
b7(i1) = b7(i2)
b7(i2) = x
End If
Next i1
Next i2
Res7(i10) = b7(1) - b7(2) + b7(3) - b7(4) + b7(5) - b7(6) + b7(7)
Return
End Sub
