' Generates Franklin Squares of order 8, magic sum 260 (Alternative)
' Tested with Office 365 under Windows 10
Sub MgcSqr8f1()
Dim a(64), b(64), c(64)
y = MsgBox("Locked", vbCritical, "Routine MgcSqr8f1")
End
n2 = 0: n9 = 0
m1 = 1: m2 = 64: s1 = 260
' Generate data
Sheets("Klad1").Select
t1 = Timer
For j64 = m1 To m2 'a(64)
If b(j64) = 0 Then b(j64) = j64: c(64) = j64 Else GoTo 640
a(64) = j64
Cells(2, 1).Value = j64
For j57 = j64 + 1 To m2 'a(57) Unique
If b(j57) = 0 Then b(j57) = j57: c(57) = j57 Else GoTo 570
a(57) = j57
Cells(3, 1).Value = j57
For j8 = j57 + 1 To m2 'a(8) Unique
If b(j8) = 0 Then b(j8) = j8: c(8) = j8 Else GoTo 80
a(8) = j8
a(1) = 0.5 * s1 - a(8) - a(57) - a(64)
If a(1) <= 0 Or a(1) > 64 Then GoTo 10
If a(1) < a(64) Then GoTo 10 ' Unique
If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
For j63 = m1 To m2 'a(63)
If b(j63) = 0 Then b(j63) = j63: c(63) = j63 Else GoTo 630
a(63) = j63
a(7) = 0.5 * s1 - a(63) - a(8) - a(64)
If a(7) <= 0 Or a(7) > 64 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
For j62 = m1 To m2 'a(62)
If b(j62) = 0 Then b(j62) = j62: c(62) = j62 Else GoTo 620
a(62) = j62
a(61) = 0.5 * s1 - a(62) - a(63) - a(64)
If a(61) <= 0 Or a(61) > 64 Then GoTo 610
If b(a(61)) = 0 Then b(a(61)) = a(61): c(61) = a(61) Else GoTo 610
a(59) = 0.5 * s1 - a(62) - a(57) - a(64)
If a(59) <= 0 Or a(59) > 64 Then GoTo 590
If b(a(59)) = 0 Then b(a(59)) = a(59): c(59) = a(59) Else GoTo 590
a(6) = -a(62) + a(8) + a(64)
If a(6) <= 0 Or a(6) > 64 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
a(5) = a(62) + a(63) - a(8)
If a(5) <= 0 Or a(5) > 64 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
a(3) = a(62) - a(8) + a(57)
If a(3) <= 0 Or a(3) > 64 Then GoTo 30
If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
For j60 = m1 To m2 'a(60)
If b(j60) = 0 Then b(j60) = j60: c(60) = j60 Else GoTo 600
a(60) = j60
a(58) = -a(60) + a(62) + a(64)
If a(58) <= 0 Or a(58) > 64 Then GoTo 580
If b(a(58)) = 0 Then b(a(58)) = a(58): c(58) = a(58) Else GoTo 580
a(4) = -a(60) + a(8) + a(64)
If a(4) <= 0 Or a(4) > 64 Then GoTo 40
If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(2) = a(60) - a(62) + a(8)
If a(2) <= 0 Or a(2) > 64 Then GoTo 20
If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
For j56 = m1 To m2 'a(56)
If b(j56) = 0 Then b(j56) = j56: c(56) = j56 Else GoTo 560
a(56) = j56
a(55) = 0.5 * s1 - a(56) - a(63) - a(64)
If a(55) <= 0 Or a(55) > 64 Then GoTo 550
If b(a(55)) = 0 Then b(a(55)) = a(55): c(55) = a(55) Else GoTo 550
a(54) = a(56) - a(62) + a(64)
If a(54) <= 0 Or a(54) > 64 Then GoTo 540
If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
a(53) = -a(56) + a(62) + a(63)
If a(53) <= 0 Or a(53) > 64 Then GoTo 530
If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
a(52) = a(56) - a(60) + a(64)
If a(52) <= 0 Or a(52) > 64 Then GoTo 520
If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
a(51) = -a(56) + a(62) + a(57)
If a(51) <= 0 Or a(51) > 64 Then GoTo 510
If b(a(51)) = 0 Then b(a(51)) = a(51): c(51) = a(51) Else GoTo 510
a(50) = a(56) + a(60) - a(62)
If a(50) <= 0 Or a(50) > 64 Then GoTo 500
If b(a(50)) = 0 Then b(a(50)) = a(50): c(50) = a(50) Else GoTo 500
a(49) = 0.5 * s1 - a(56) - a(57) - a(64)
If a(49) <= 0 Or a(49) > 64 Then GoTo 490
If b(a(49)) = 0 Then b(a(49)) = a(49): c(49) = a(49) Else GoTo 490
For j48 = m1 To m2 'a(48)
If b(j48) = 0 Then b(j48) = j48: c(48) = j48 Else GoTo 480
a(48) = j48
a(47) = -a(48) + a(63) + a(64)
If a(47) <= 0 Or a(47) > 64 Then GoTo 470
If b(a(47)) = 0 Then b(a(47)) = a(47): c(47) = a(47) Else GoTo 470
a(46) = a(48) + a(62) - a(64)
If a(46) <= 0 Or a(46) > 64 Then GoTo 460
If b(a(46)) = 0 Then b(a(46)) = a(46): c(46) = a(46) Else GoTo 460
a(45) = 0.5 * s1 - a(48) - a(62) - a(63)
If a(45) <= 0 Or a(45) > 64 Then GoTo 450
If b(a(45)) = 0 Then b(a(45)) = a(45): c(45) = a(45) Else GoTo 450
a(44) = a(48) + a(60) - a(64)
If a(44) <= 0 Or a(44) > 64 Then GoTo 440
If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
a(43) = 0.5 * s1 - a(48) - a(62) - a(57)
If a(43) <= 0 Or a(43) > 64 Then GoTo 430
If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(42) = a(48) - a(60) + a(62)
If a(42) <= 0 Or a(42) > 64 Then GoTo 420
If b(a(42)) = 0 Then b(a(42)) = a(42): c(42) = a(42) Else GoTo 420
a(41) = -a(48) + a(57) + a(64)
If a(41) <= 0 Or a(41) > 64 Then GoTo 410
If b(a(41)) = 0 Then b(a(41)) = a(41): c(41) = a(41) Else GoTo 410
a(40) = 0.5 * s1 - a(48) - a(56) - a(64)
If a(40) <= 0 Or a(40) > 64 Then GoTo 400
If b(a(40)) = 0 Then b(a(40)) = a(40): c(40) = a(40) Else GoTo 400
a(39) = a(48) + a(56) - a(63)
If a(39) <= 0 Or a(39) > 64 Then GoTo 390
If b(a(39)) = 0 Then b(a(39)) = a(39): c(39) = a(39) Else GoTo 390
a(38) = 0.5 * s1 - a(48) - a(56) - a(62)
If a(38) <= 0 Or a(38) > 64 Then GoTo 380
If b(a(38)) = 0 Then b(a(38)) = a(38): c(38) = a(38) Else GoTo 380
a(37) = -0.5 * s1 + a(48) + a(56) + a(62) + a(63) + a(64)
If a(37) <= 0 Or a(37) > 64 Then GoTo 370
If b(a(37)) = 0 Then b(a(37)) = a(37): c(37) = a(37) Else GoTo 370
a(36) = 0.5 * s1 - a(48) - a(56) - a(60)
If a(36) <= 0 Or a(36) > 64 Then GoTo 360
If b(a(36)) = 0 Then b(a(36)) = a(36): c(36) = a(36) Else GoTo 360
a(35) = -0.5 * s1 + a(48) + a(56) + a(62) + a(57) + a(64)
If a(35) <= 0 Or a(35) > 64 Then GoTo 350
If b(a(35)) = 0 Then b(a(35)) = a(35): c(35) = a(35) Else GoTo 350
a(34) = 0.5 * s1 - a(48) - a(56) + a(60) - a(62) - a(64)
If a(34) <= 0 Or a(34) > 64 Then GoTo 340
If b(a(34)) = 0 Then b(a(34)) = a(34): c(34) = a(34) Else GoTo 340
a(33) = a(48) + a(56) - a(57)
If a(33) <= 0 Or a(33) > 64 Then GoTo 330
If b(a(33)) = 0 Then b(a(33)) = a(33): c(33) = a(33) Else GoTo 330
a(24) = 0.5 * s1 - a(48) - a(8) - a(64)
If a(24) <= 0 Or a(24) > 64 Then GoTo 240
If b(a(24)) = 0 Then b(a(24)) = a(24): c(24) = a(24) Else GoTo 240
a(23) = a(48) - a(63) + a(8)
If a(23) <= 0 Or a(23) > 64 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = 0.5 * s1 - a(48) - a(62) - a(8)
If a(22) <= 0 Or a(22) > 64 Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = -0.5 * s1 + a(48) + a(62) + a(63) + a(8) + a(64)
If a(21) <= 0 Or a(21) > 64 Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(20) = 0.5 * s1 - a(48) - a(60) - a(8)
If a(20) <= 0 Or a(20) > 64 Then GoTo 200
If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = -0.5 * s1 + a(48) + a(62) + a(8) + a(57) + a(64)
If a(19) <= 0 Or a(19) > 64 Then GoTo 190
If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(18) = 0.5 * s1 - a(48) + a(60) - a(62) - a(8) - a(64)
If a(18) <= 0 Or a(18) > 64 Then GoTo 180
If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(17) = a(48) + a(8) - a(57)
If a(17) <= 0 Or a(17) > 64 Then GoTo 170
If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
For j32 = m1 To m2 'a(32)
If b(j32) = 0 Then b(j32) = j32: c(32) = j32 Else GoTo 320
a(32) = j32
a(31) = -a(32) + a(63) + a(64)
If a(31) <= 0 Or a(31) > 64 Then GoTo 310
If b(a(31)) = 0 Then b(a(31)) = a(31): c(31) = a(31) Else GoTo 310
a(30) = a(32) + a(62) - a(64)
If a(30) <= 0 Or a(30) > 64 Then GoTo 300
If b(a(30)) = 0 Then b(a(30)) = a(30): c(30) = a(30) Else GoTo 300
a(29) = 0.5 * s1 - a(32) - a(62) - a(63)
If a(29) <= 0 Or a(29) > 64 Then GoTo 290
If b(a(29)) = 0 Then b(a(29)) = a(29): c(29) = a(29) Else GoTo 290
a(28) = a(32) + a(60) - a(64)
If a(28) <= 0 Or a(28) > 64 Then GoTo 280
If b(a(28)) = 0 Then b(a(28)) = a(28): c(28) = a(28) Else GoTo 280
a(27) = 0.5 * s1 - a(32) - a(62) - a(57)
If a(27) <= 0 Or a(27) > 64 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(26) = a(32) - a(60) + a(62)
If a(26) <= 0 Or a(26) > 64 Then GoTo 260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(25) = -a(32) + a(57) + a(64)
If a(25) <= 0 Or a(25) > 64 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(16) = -a(32) + a(48) + a(64)
If a(16) <= 0 Or a(16) > 64 Then GoTo 160
If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
a(15) = a(32) - a(48) + a(63)
If a(15) <= 0 Or a(15) > 64 Then GoTo 150
If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
a(14) = -a(32) + a(48) + a(62)
If a(14) <= 0 Or a(14) > 64 Then GoTo 140
If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = 0.5 * s1 + a(32) - a(48) - a(62) - a(63) - a(64)
If a(13) <= 0 Or a(13) > 64 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(12) = -a(32) + a(48) + a(60)
If a(12) <= 0 Or a(12) > 64 Then GoTo 120
If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
a(11) = 0.5 * s1 + a(32) - a(48) - a(62) - a(57) - a(64)
If a(11) <= 0 Or a(11) > 64 Then GoTo 110
If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
a(10) = -a(32) + a(48) - a(60) + a(62) + a(64)
If a(10) <= 0 Or a(10) > 64 Then GoTo 100
If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(9) = a(32) - a(48) + a(57)
If a(9) <= 0 Or a(9) > 64 Then GoTo 90
If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 5 '(Back Check)
n9 = n9 + 1
Cells(1, 1).Value = n9 'Counting
' GoSub 650 'Print results (squares)
' GoSub 645 'Print results (selected numbers)
5
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(12)) = 0: c(12) = 0
120 b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(15)) = 0: c(15) = 0
150 b(c(16)) = 0: c(16) = 0
160 b(c(25)) = 0: c(25) = 0
250 b(c(26)) = 0: c(26) = 0
260 b(c(27)) = 0: c(27) = 0
270 b(c(28)) = 0: c(28) = 0
280 b(c(29)) = 0: c(29) = 0
290 b(c(30)) = 0: c(30) = 0
300 b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(17)) = 0: c(17) = 0
170 b(c(18)) = 0: c(18) = 0
180 b(c(19)) = 0: c(19) = 0
190 b(c(20)) = 0: c(20) = 0
200 b(c(21)) = 0: c(21) = 0
210 b(c(22)) = 0: c(22) = 0
220 b(c(23)) = 0: c(23) = 0
230 b(c(24)) = 0: c(24) = 0
240 b(c(33)) = 0: c(33) = 0
330 b(c(34)) = 0: c(34) = 0
340 b(c(35)) = 0: c(35) = 0
350 b(c(36)) = 0: c(36) = 0
360 b(c(37)) = 0: c(37) = 0
370 b(c(38)) = 0: c(38) = 0
380 b(c(39)) = 0: c(39) = 0
390 b(c(40)) = 0: c(40) = 0
400 b(c(41)) = 0: c(41) = 0
410 b(c(42)) = 0: c(42) = 0
420 b(c(43)) = 0: c(43) = 0
430 b(c(44)) = 0: c(44) = 0
440 b(c(45)) = 0: c(45) = 0
450 b(c(46)) = 0: c(46) = 0
460 b(c(47)) = 0: c(47) = 0
470 b(c(48)) = 0: c(48) = 0
480 Next j48
b(c(49)) = 0: c(49) = 0
490 b(c(50)) = 0: c(50) = 0
500 b(c(51)) = 0: c(51) = 0
510 b(c(52)) = 0: c(52) = 0
520 b(c(53)) = 0: c(53) = 0
530 b(c(54)) = 0: c(54) = 0
540 b(c(55)) = 0: c(55) = 0
550 b(c(56)) = 0: c(56) = 0
560 Next j56
b(c(2)) = 0: c(2) = 0
20 b(c(4)) = 0: c(4) = 0
40 b(c(58)) = 0: c(58) = 0
580 b(c(60)) = 0: c(60) = 0
600 Next j60
b(c(3)) = 0: c(3) = 0
30 b(c(5)) = 0: c(5) = 0
50 b(c(6)) = 0: c(6) = 0
60 b(c(59)) = 0: c(59) = 0
590 b(c(61)) = 0: c(61) = 0
610 b(c(62)) = 0: c(62) = 0
620 Next j62
b(c(7)) = 0: c(7) = 0
70 b(c(63)) = 0: c(63) = 0
630 Next j63
b(c(1)) = 0: c(1) = 0
10 b(c(8)) = 0: c(8) = 0
80 Next j8
b(c(57)) = 0: c(57) = 0
570 Next j57
b(c(64)) = 0: c(64) = 0
640 Next j64
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine MgcSqr8f1")
End
' Print results (selected numbers)
645 For i1 = 1 To 64
Cells(n9, i1).Value = a(i1)
Next i1
Return
' Print results (squares)
650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 9: k2 = 0
Else
If n9 > 1 Then k2 = k2 + 9
End If
Cells(k1 + 1, k2 + 1).Select
i3 = 0
For i1 = 1 To 8
For i2 = 1 To 8
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers
800 fl1 = 1
For j1 = 1 To 64
a2 = a(j1)
For j2 = (1 + j1) To 64
If a2 = a(j2) Then fl1 = 0: GoTo 850
Next j2
Next j1
850 Return
End Sub
