' Completess Inlaid Magic Squares of order 15, Integers 1 ... 225 (Corner Squares)
' Step 1: Generate Btm/Left Associated Rectangle
' Step 2: Add result to Input Sheet
'
Generate Top/Right Associated Rectangle (Transposed)
' Tested with Office 365 under Windows 10
Sub MgcSqrs15c()
Dim a1(225), a(225), b1(225), b(225), c(225)
Dim a15(225)
y = MsgBox("Locked", vbCritical, "Routine MgcSqrs15c")
End
n1 = 0: n2 = 0: n3 = 0: k1 = 1: k2 = 1: n9 = 0: n10 = 0
s1 = 1695: Pr15 = 226:
s4 = 2 * Pr15: s3 = 3 * Pr15 / 2:
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
' Define Available Integers based on sheet 'Input15'
For i1 = 1 To 225 'Range
b1(i1) = i1
Next i1
i3 = 0 'Available Integers
For i1 = 2 To 16
For i2 = 2 To 16
x = Sheets("Input15").Cells(i1, i2).Value
b1(x) = 0
i3 = i3 + 1: a15(i3) = x
Next i2
Next i1
i3 = 0
For i1 = 1 To 225
If b1(i1) <> 0 Then
i3 = i3 + 1: a1(i3) = i1
End If
Next i1
m1 = 1: m2 = i3
' Corner Rectangles
' Sub Sqr 4 x 4
For j56 = m1 To m2 / 2 'a(56)
If b1(a1(j56)) = 0 Then GoTo 560
If b(a1(j56)) = 0 Then b(a1(j56)) = a1(j56): c(56) = a1(j56) Else GoTo 560
a(56) = a1(j56)
a(1) = Pr15 - a(56): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j55 = m1 To m2 'a(55)
If b1(a1(j55)) = 0 Then GoTo 550
If b(a1(j55)) = 0 Then b(a1(j55)) = a1(j55): c(55) = a1(j55) Else GoTo 550
a(55) = a1(j55)
a(2) = Pr15 - a(55): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j54 = m1 To m2 'a(54)
If b1(a1(j54)) = 0 Then GoTo 540
If b(a1(j54)) = 0 Then b(a1(j54)) = a1(j54): c(54) = a1(j54) Else GoTo 540
a(54) = a1(j54)
a(3) = Pr15 - a(54): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(53) = s4 - a(54) - a(55) - a(56)
If a(53) < a1(m1) Or a(53) > a1(m2) Then GoTo 530
If b1(a(53)) = 0 Then GoTo 530
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(4) = Pr15 - a(53): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
For j49 = m2 To m1 Step -1 'a(49)
If b1(a1(j49)) = 0 Then GoTo 490
If b(a1(j49)) = 0 Then b(a1(j49)) = a1(j49): c(49) = a1(j49) Else GoTo 490
a(49) = a1(j49)
a(8) = Pr15 - a(49): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j48 = m2 To m1 Step -1 'a(48)
If b1(a1(j48)) = 0 Then GoTo 480
If b(a1(j48)) = 0 Then b(a1(j48)) = a1(j48): c(48) = a1(j48) Else GoTo 480
a(48) = a1(j48)
a(9) = Pr15 - a(48): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j47 = m2 To m1 Step -1 'a(47)
If b1(a1(j47)) = 0 Then GoTo 470
If b(a1(j47)) = 0 Then b(a1(j47)) = a1(j47): c(47) = a1(j47) Else GoTo 470
a(47) = a1(j47)
a(10) = Pr15 - a(47): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(46) = s4 - a(47) - a(48) - a(49)
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(11) = Pr15 - a(46): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j42 = m1 To m2 'a(42)
If b1(a1(j42)) = 0 Then GoTo 420
If b(a1(j42)) = 0 Then b(a1(j42)) = a1(j42): c(42) = a1(j42) Else GoTo 420
a(42) = a1(j42)
a(15) = Pr15 - a(42): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j41 = m1 To m2 'a(41)
If b1(a1(j41)) = 0 Then GoTo 410
If b(a1(j41)) = 0 Then b(a1(j41)) = a1(j41): c(41) = a1(j41) Else GoTo 410
a(41) = a1(j41)
a(16) = Pr15 - a(41): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
For j40 = m1 To m2 'a(40)
If b1(a1(j40)) = 0 Then GoTo 400
If b(a1(j40)) = 0 Then b(a1(j40)) = a1(j40): c(40) = a1(j40) Else GoTo 400
a(40) = a1(j40)
a(17) = Pr15 - a(40): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(39) = s4 - a(40) - a(41) - a(42)
If a(39) < a1(m1) Or a(39) > a1(m2) Then GoTo 390
If b1(a(39)) = 0 Then GoTo 390
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(18) = Pr15 - a(39): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(35) = s4 - a(42) - a(49) - a(56)
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(22) = Pr15 - a(35): If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(34) = s4 - a(41) - a(48) - a(55)
If a(34) < a1(m1) Or a(34) > a1(m2) Then GoTo 340
If b1(a(34)) = 0 Then GoTo 340
If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(23) = Pr15 - a(34): If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(33) = s4 - a(40) - a(47) - a(54)
If a(33) < a1(m1) Or a(33) > a1(m2) Then GoTo 330
If b1(a(33)) = 0 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(24) = Pr15 - a(33): If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(32) = s4 - a(39) - a(46) - a(53)
If a(32) < a1(m1) Or a(32) > a1(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(25) = Pr15 - a(32): If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
' Sub Rectangle 3 x 3
For j52 = m1 To m2 'a(52)
If b1(a1(j52)) = 0 Then GoTo 520
If b(a1(j52)) = 0 Then b(a1(j52)) = a1(j52): c(52) = a1(j52) Else GoTo 520
a(52) = a1(j52)
a(5) = Pr15 - a(52): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j51 = m1 To m2 'a(51)
If b1(a1(j51)) = 0 Then GoTo 510
If b(a1(j51)) = 0 Then b(a1(j51)) = a1(j51): c(51) = a1(j51) Else GoTo 510
a(51) = a1(j51)
a(50) = s3 - a(51) - a(52)
If a(50) < a1(m1) Or a(50) > a1(m2) Then GoTo 500
If b1(a(50)) = 0 Then GoTo 500
If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
a(7) = Pr15 - a(50): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
a(6) = Pr15 - a(51): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j45 = m2 To m1 Step -1 'a(45)
If b1(a1(j45)) = 0 Then GoTo 450
If b(a1(j45)) = 0 Then b(a1(j45)) = a1(j45): c(45) = a1(j45) Else GoTo 450
a(45) = a1(j45)
a(12) = Pr15 - a(45): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j44 = m2 To m1 Step -1 'a(44)
If b1(a1(j44)) = 0 Then GoTo 440
If b(a1(j44)) = 0 Then b(a1(j44)) = a1(j44): c(44) = a1(j44) Else GoTo 440
a(44) = a1(j44)
a(43) = s3 - 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(14) = Pr15 - a(43): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = Pr15 - a(44): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j38 = m1 To m2 'a(38)
If b1(a1(j38)) = 0 Then GoTo 380
If b(a1(j38)) = 0 Then b(a1(j38)) = a1(j38): c(38) = a1(j38) Else GoTo 380
a(38) = a1(j38)
a(19) = Pr15 - a(38): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
For j37 = m1 To m2 'a(37)
If b1(a1(j37)) = 0 Then GoTo 370
If b(a1(j37)) = 0 Then b(a1(j37)) = a1(j37): c(37) = a1(j37) Else GoTo 370
a(37) = a1(j37)
a(36) = s3 - 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
a(21) = Pr15 - a(36): If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = Pr15 - a(37): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(31) = s4 - a(38) - a(45) - a(52)
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(26) = Pr15 - a(31): If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(30) = s4 - a(37) - a(44) - a(51)
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(27) = Pr15 - a(30): If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(29) = s4 - a(36) - a(43) - a(50)
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(28) = Pr15 - a(29): If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
GoSub 2500: If fl1 = 0 Then GoTo 5 'Double Check Identical Integers a15()
n9 = n9 + 1: GoSub 2750: End
5
b(c(28)) = 0: c(28) = 0
280 b(c(29)) = 0: c(29) = 0
290
b(c(27)) = 0: c(27) = 0
270 b(c(30)) = 0: c(30) = 0
300
b(c(26)) = 0: c(26) = 0
260 b(c(31)) = 0: c(31) = 0
310
b(c(20)) = 0: c(20) = 0
200 b(c(21)) = 0: c(21) = 0
210 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 Next j37
b(c(19)) = 0: c(19) = 0
190 b(c(38)) = 0: c(38) = 0
380 Next j38
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 Next j44
b(c(12)) = 0: c(12) = 0
120 b(c(45)) = 0: c(45) = 0
450 Next j45
b(c(6)) = 0: c(6) = 0
60 b(c(7)) = 0: c(7) = 0
70 b(c(50)) = 0: c(50) = 0
500 b(c(51)) = 0: c(51) = 0
510 Next j51
b(c(5)) = 0: c(5) = 0
50 b(c(52)) = 0: c(52) = 0
520 Next j52
b(c(25)) = 0: c(25) = 0
250 b(c(32)) = 0: c(32) = 0
320 b(c(24)) = 0: c(24) = 0
240 b(c(33)) = 0: c(33) = 0
330 b(c(23)) = 0: c(23) = 0
230 b(c(34)) = 0: c(34) = 0
340 b(c(22)) = 0: c(22) = 0
220 b(c(35)) = 0: c(35) = 0
350 b(c(18)) = 0: c(18) = 0
180 b(c(39)) = 0: c(39) = 0
390 b(c(17)) = 0: c(17) = 0
170 b(c(40)) = 0: c(40) = 0
400 Next j40
b(c(16)) = 0: c(16) = 0
160 b(c(41)) = 0: c(41) = 0
410 Next j41
b(c(15)) = 0: c(15) = 0
150 b(c(42)) = 0: c(42) = 0
420 Next j42
b(c(11)) = 0: c(11) = 0
110 b(c(46)) = 0: c(46) = 0
460 b(c(10)) = 0: c(10) = 0
100 b(c(47)) = 0: c(47) = 0
470 Next j47
b(c(9)) = 0: c(9) = 0
90 b(c(48)) = 0: c(48) = 0
480 Next j48
b(c(8)) = 0: c(8) = 0
80 b(c(49)) = 0: c(49) = 0
490 Next j49
b(c(4)) = 0: c(4) = 0
40 b(c(53)) = 0: c(53) = 0
530 b(c(3)) = 0: c(3) = 0
30 b(c(54)) = 0: c(54) = 0
540 Next j54
b(c(2)) = 0: c(2) = 0
20 b(c(55)) = 0: c(55) = 0
550 Next j55
b(c(1)) = 0: c(1) = 0
10 b(c(56)) = 0: c(56) = 0
560 Next j56
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqrs15c")
End
' Exclude solutions with identical numbers
2500 fl1 = 1
For i10 = 1 To 225
c2 = a15(i10): If c2 = 0 Then GoTo 2510
For i20 = (1 + i10) To 225
If c2 = a15(i20) Then fl1 = 0: Return
Next i20
2510 Next i10
Return
' Print results (lines)
2640
For i1 = 1 To 225
Cells(n9, i1).Value = a15(i1)
Next i1
Cells(n9, 226).Value = s1
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 3 Then
n2 = 1: k1 = k1 + 16: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 16
End If
'' Cells(2, 1).Value = n9
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
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
' Print results (rectangles)
2750 n2 = n2 + 1
If n2 = 3 Then
n2 = 1: k1 = k1 + 16: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 16
End If
'' Cells(2, 1).Value = n9
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
i3 = 0
For i1 = 1 To 8
For i2 = 1 To 7
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
