' Generates Simple Latin Cubes of order 4 for integers 0 thru 7
' Horizontal Associated Magic Planes
' Tested with Office 365 under Windows 10
Sub SudCube41()
Dim a(64), b(4), s(8)
y = MsgBox("Locked", vbCritical, "Routine SudCube41")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
m1 = 0: m2 = 7: s1 = 14
' Generate data
Sheets("Klad1").Select
t1 = Timer
For j64 = m1 To m2 'a(64)
a(64) = j64
For j63 = m1 To m2 'a(63)
a(63) = j63
For j62 = m1 To m2 'a(62)
a(62) = j62
a(61) = s1 - a(62) - a(63) - a(64): If a(61) < m1 Or a(61) > m2 Then GoTo 620
For j60 = m1 To m2 'a(60)
a(60) = j60
a(59) = s1 - a(60) - a(63) - a(64): If a(59) < m1 Or a(59) > m2 Then GoTo 600
a(58) = s1 - a(60) - a(62) - a(64): If a(58) < m1 Or a(58) > m2 Then GoTo 600
a(57) = s1 - a(58) - a(59) - a(60): If a(57) < m1 Or a(57) > m2 Then GoTo 600
' Complete Top Square
a(56) = s1 / 2 - a(57): a(55) = s1 / 2 - a(58):
a(54) = s1 / 2 - a(59): a(53) = s1 / 2 - a(60):
a(52) = s1 / 2 - a(61): a(51) = s1 / 2 - a(62):
a(50) = s1 / 2 - a(63): a(49) = s1 / 2 - a(64):
' Check Top Square
b(1) = a(49): b(2) = a(50): b(3) = a(51): b(4) = a(52): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(53): b(2) = a(54): b(3) = a(55): b(4) = a(56): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(57): b(2) = a(58): b(3) = a(59): b(4) = a(60): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(61): b(2) = a(62): b(3) = a(63): b(4) = a(64): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(49): b(2) = a(53): b(3) = a(57): b(4) = a(61): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(50): b(2) = a(54): b(3) = a(58): b(4) = a(62): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(51): b(2) = a(55): b(3) = a(59): b(4) = a(63): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(52): b(2) = a(56): b(3) = a(60): b(4) = a(64): GoSub 860: If fl1 = 0 Then GoTo 600
b(1) = a(49): b(2) = a(54): b(3) = a(59): b(4) = a(64): GoSub 875: If fl1 = 0 Then GoTo 600
b(1) = a(52): b(2) = a(55): b(3) = a(58): b(4) = a(61): GoSub 875: If fl1 = 0 Then GoTo 600
For j48 = m1 To m2 'a(48)
a(48) = j48
For j47 = m1 To m2 'a(47)
a(47) = j47
For j46 = m1 To m2 'a(46)
a(46) = j46
a(45) = s1 - a(46) - a(47) - a(48): If a(45) < m1 Or a(45) > m2 Then GoTo 460
For j44 = m1 To m2 'a(44)
a(44) = j44
a(43) = s1 - a(44) - a(47) - a(48): If a(43) < m1 Or a(43) > m2 Then GoTo 440
a(42) = s1 - a(44) - a(46) - a(48): If a(42) < m1 Or a(42) > m2 Then GoTo 440
a(41) = s1 - a(42) - a(43) - a(44): If a(41) < m1 Or a(41) > m2 Then GoTo 440
For j32 = m1 To m2 'a(32)
a(32) = j32
a(31) = s1 - a(32) - a(46) - a(48) + a(61) - a(64):
If a(31) < m1 Or a(31) > m2 Then GoTo 320
a(28) = -a(32) + a(44) - a(45) + a(62) + a(63):
If a(28) < m1 Or a(28) > m2 Then GoTo 320
a(27) = a(32) - a(44) - a(47) + 2 * a(64):
If a(27) < m1 Or a(27) > m2 Then GoTo 320
a(16) = s1 - a(32) - a(48) - a(64): If a(16) < m1 Or a(16) > m2 Then GoTo 320
a(15) = s1 - a(31) - a(47) - a(63): If a(15) < m1 Or a(15) > m2 Then GoTo 320
For j30 = m1 To m2 'a(30)
a(30) = j30
a(29) = s1 - a(30) - a(31) - a(32): If a(29) < m1 Or a(29) > m2 Then GoTo 300
a(26) = s1 - a(28) - a(30) - a(32): If a(26) < m1 Or a(26) > m2 Then GoTo 300
a(25) = s1 - a(26) - a(27) - a(28): If a(25) < m1 Or a(25) > m2 Then GoTo 300
a(14) = s1 - a(30) - a(46) - a(62): If a(14) < m1 Or a(14) > m2 Then GoTo 300
a(13) = a(30) + a(47) - a(64): If a(13) < m1 Or a(13) > m2 Then GoTo 300
a(12) = s1 - a(28) - a(44) - a(60): If a(12) < m1 Or a(12) > m2 Then GoTo 300
a(11) = s1 - a(27) - a(43) - a(59): If a(11) < m1 Or a(11) > m2 Then GoTo 300
a(10) = s1 - a(26) - a(42) - a(58): If a(10) < m1 Or a(10) > m2 Then GoTo 300
a(9) = s1 - a(25) - a(41) - a(57): If a(9) < m1 Or a(9) > m2 Then GoTo 300
a(40) = s1 / 2 - a(41): a(24) = s1 / 2 - a(25): a(8) = s1 / 2 - a(9):
a(39) = s1 / 2 - a(42): a(23) = s1 / 2 - a(26): a(7) = s1 / 2 - a(10):
a(38) = s1 / 2 - a(43): a(22) = s1 / 2 - a(27): a(6) = s1 / 2 - a(11):
a(37) = s1 / 2 - a(44): a(21) = s1 / 2 - a(28): a(5) = s1 / 2 - a(12):
a(36) = s1 / 2 - a(45): a(20) = s1 / 2 - a(29): a(4) = s1 / 2 - a(13):
a(35) = s1 / 2 - a(46): a(19) = s1 / 2 - a(30): a(3) = s1 / 2 - a(14):
a(34) = s1 / 2 - a(47): a(18) = s1 / 2 - a(31): a(2) = s1 / 2 - a(15):
a(33) = s1 / 2 - a(48): a(17) = s1 / 2 - a(32): a(1) = s1 / 2 - a(16):
' Exclude solutions with identical numbers in rows, colums or pillars
GoSub 800: If fl1 = 0 Then GoTo 300 'rows, colums or pillars
GoSub 900: If fl1 = 0 Then GoTo 300 'Valid (Semi) Latin Cube
n9 = n9 + 1: GoSub 740 'Print results (selected numbers)
' n9 = n9 + 1: GoSub 750 'Print results (planes 1, 2, 3, 4)
' n9 = n9 + 1: Cells(1, 1).Value = n9 'Counting
300 Next j30
320 Next j32
440 Next j44
460 Next j46
470 Next j47
480 Next j48
600 Next j60
620 Next j62
630 Next j63
640 Next j64
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine SudCube41")
End
' Print results (selected numbers)
740 For i1 = 1 To 64
Cells(n9, i1).Value = a(i1)
Next i1
Cells(1, 67).Value = n9
Return
' Print results (planes 11, 12, 13 and 14)
750 n2 = n2 + 1
If n2 = 9 Then
n2 = 1: k1 = k1 + 20: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 5
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(n9)
For i0 = 1 To 4
i3 = (4 - i0) * 16
For i1 = 1 To 4
For i2 = 1 To 4
i3 = i3 + 1
Cells(k1 + i1 + (i0 - 1) * 5, k2 + i2).Value = a(i3)
Next i2
Next i1
Next i0
Return
' Exclude solutions with identical numbers in rows, colums or pillars
800 fl1 = 1
' Rows
i1 = -3
For i0 = 1 To 16
i1 = i1 + 4
b(1) = a(i1): b(2) = a(i1 + 1): b(3) = a(i1 + 2): b(4) = a(i1 + 3)
GoSub 860
If fl1 = 0 Then Return
Next i0
' Columns
i1 = 0: i2 = 0
For i0 = 1 To 16
i1 = i1 + 1
b(1) = a(i1): b(2) = a(i1 + 4): b(3) = a(i1 + 8): b(4) = a(i1 + 12)
i2 = i2 + 1: If i2 = 4 Then i2 = 0: i1 = i1 + 12
GoSub 860
If fl1 = 0 Then Return
Next i0
' Pillars
i1 = 0: i2 = 0
For i0 = 1 To 16
i1 = i0
b(1) = a(i1): b(2) = a(i1 + 16): b(3) = a(i1 + 32): b(4) = a(i1 + 48)
GoSub 860
If fl1 = 0 Then Return
Next i0
' Space Diagonals
b(1) = a(1): b(2) = a(22): b(3) = a(43): b(4) = a(64): GoSub 860: If fl1 = 0 Then Return
b(1) = a(4): b(2) = a(23): b(3) = a(42): b(4) = a(61): GoSub 860: If fl1 = 0 Then Return
b(1) = a(13): b(2) = a(26): b(3) = a(39): b(4) = a(52): GoSub 860: If fl1 = 0 Then Return
b(1) = a(16): b(2) = a(27): b(3) = a(38): b(4) = a(49): GoSub 860: If fl1 = 0 Then Return
' Diagonals Hor Magic Planes
b(1) = a(1): b(2) = a(6): b(3) = a(11): b(4) = a(16): GoSub 875: If fl1 = 0 Then Return
b(1) = a(4): b(2) = a(7): b(3) = a(10): b(4) = a(13): GoSub 875: If fl1 = 0 Then Return
b(1) = a(17): b(2) = a(22): b(3) = a(27): b(4) = a(32): GoSub 875: If fl1 = 0 Then Return
b(1) = a(20): b(2) = a(23): b(3) = a(26): b(4) = a(29): GoSub 875: If fl1 = 0 Then Return
b(1) = a(33): b(2) = a(38): b(3) = a(43): b(4) = a(48): GoSub 875: If fl1 = 0 Then Return
b(1) = a(36): b(2) = a(39): b(3) = a(42): b(4) = a(45): GoSub 875: If fl1 = 0 Then Return
b(1) = a(49): b(2) = a(54): b(3) = a(59): b(4) = a(64): GoSub 875: If fl1 = 0 Then Return
b(1) = a(52): b(2) = a(55): b(3) = a(58): b(4) = a(61): GoSub 875: If fl1 = 0 Then Return
Return
860 fl1 = 1
For j1 = 1 To 4
b2 = b(j1)
For j2 = (1 + j1) To 4
If b2 = b(j2) Then fl1 = 0: Return
Next j2
Next j1
GoSub 875 'Check suitable for Prime Numbers
Return
' Check suitable for Prime Numbers
875 fl1 = 1
Erase s
For j1 = 1 To 4
s(b(j1) + 1) = s(b(j1) + 1) + 1
Next j1
For j1 = 1 To 4
If s(j1) <> s(9 - j1) Then fl1 = 0: Return
Next j1
Return
' Valid (Semi) Latin Cube
900 fl1 = 1
Erase s
For i1 = 1 To 64
s(a(i1) + 1) = s(a(i1) + 1) + 1
Next i1
For i1 = 1 To 8
If s(i1) <> 8 Then fl1 = 0: Return
Next i1
Return
End Sub
