' Generates SelfOrthogonal Latin Diagonal Squares (9 x 9)
' Based on Idempotent Squares (Permutations)
' Tested with Office 365 under Windows 11
Sub SelfOrth9c()
Dim a1(9), a2(81), a(81)
Dim b(81), c(81), c1(81), s(81)
y = MsgBox("Locked", vbCritical, "Routine SelfOrth9a")
End
n2 = 0: n9 = 0: k1 = 1: k2 = 1
s1 = 36: s2 = 8: s4 = 2 * s2: s5 = 5 * s2 / 2: s3 = 3 * s2 / 2
Sheets("Klad1").Select
t1 = Timer
ShtNm1 = "IdmpAss9": n30 = 23232 'Idempotent, Associated
'' ShtNm2 = "MgcLns9a": n31 = 362880 'Latin Series
ShtNm2 = "MgcLns9b": n31 = 384 'Latin Series, Balanced
For j100 = 2 To n30 + 1 'Idempotent Squares
For i1 = 1 To 81
a2(i1) = Sheets(ShtNm1).Cells(j100, i1).Value
Next i1
For j200 = 1 To n31 'Series order 9
For i1 = 1 To 9
a1(i1) = Sheets(ShtNm2).Cells(j200, i1).Value
Next i1
For i1 = 1 To 81
i2 = a2(i1) + 1 'Index in a1()
a(i1) = a1(i2)
Next i1
'' GoSub 1050: If fl1 = 0 Then GoTo 5 'Check Associated
'' GoSub 1100: If fl1 = 0 Then GoTo 5 'Check Pan Diagonals
GoSub 1170: If fl1 = 0 Then GoTo 5 'Check Diamond Inlay (3 x 3)
'' GoSub 1200: If fl1 = 0 Then GoTo 5 'Check Diamond Inlay (4 x 4)
'' GoSub 1250: If fl1 = 0 Then GoTo 5 'Check Diamond Inlay (5 x 5)
'' GoSub 1300: If fl1 = 0 Then GoTo 5 'Check Square Inlay (5 x 5)
'' GoSub 1350: If fl1 = 0 Then GoTo 5 'Check Row/3 and Clmn/3
GoSub 1450: If fl1 = 0 Then GoTo 5 'Check Compact (3 x 3)
n9 = n9 + 1: GoSub 2650: GoTo 1001 'Print Squares
Cells(1, 1).Value = n9
5
2000 Next j200
1000 Next j100
1001
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s1)
y = MsgBox(t10, 0, "Routine SelfOrth9c")
End
' Check Compact (3 x 3)
1450 fl1 = 1
'Clmn 1
s(1) = a(1) + a(10) + a(19) + a(2) + a(11) + a(20) + a(3) + a(12) + a(21):
s(2) = a(2) + a(11) + a(20) + a(3) + a(12) + a(21) + a(4) + a(13) + a(22):
s(3) = a(3) + a(12) + a(21) + a(4) + a(13) + a(22) + a(5) + a(14) + a(23):
s(4) = a(4) + a(13) + a(22) + a(5) + a(14) + a(23) + a(6) + a(15) + a(24):
s(5) = a(5) + a(14) + a(23) + a(6) + a(15) + a(24) + a(7) + a(16) + a(25):
s(6) = a(6) + a(15) + a(24) + a(7) + a(16) + a(25) + a(8) + a(17) + a(26):
s(7) = a(7) + a(16) + a(25) + a(8) + a(17) + a(26) + a(9) + a(18) + a(27):
s(8) = a(8) + a(17) + a(26) + a(9) + a(18) + a(27) + a(1) + a(10) + a(19):
s(9) = a(9) + a(18) + a(27) + a(1) + a(10) + a(19) + a(2) + a(11) + a(20):
'Clmn 2
s(10) = a(10) + a(19) + a(28) + a(11) + a(20) + a(29) + a(12) + a(21) + a(30):
s(11) = a(11) + a(20) + a(29) + a(12) + a(21) + a(30) + a(13) + a(22) + a(31):
s(12) = a(12) + a(21) + a(30) + a(13) + a(22) + a(31) + a(14) + a(23) + a(32):
s(13) = a(13) + a(22) + a(31) + a(14) + a(23) + a(32) + a(15) + a(24) + a(33):
s(14) = a(14) + a(23) + a(32) + a(15) + a(24) + a(33) + a(16) + a(25) + a(34):
s(15) = a(15) + a(24) + a(33) + a(16) + a(25) + a(34) + a(17) + a(26) + a(35):
s(16) = a(16) + a(25) + a(34) + a(17) + a(26) + a(35) + a(18) + a(27) + a(36):
s(17) = a(17) + a(26) + a(35) + a(18) + a(27) + a(36) + a(10) + a(19) + a(28):
s(18) = a(18) + a(27) + a(36) + a(10) + a(19) + a(28) + a(11) + a(20) + a(29):
'Clmn 3
s(19) = a(19) + a(28) + a(37) + a(20) + a(29) + a(38) + a(21) + a(30) + a(39):
s(20) = a(20) + a(29) + a(38) + a(21) + a(30) + a(39) + a(22) + a(31) + a(40):
s(21) = a(21) + a(30) + a(39) + a(22) + a(31) + a(40) + a(23) + a(32) + a(41):
s(22) = a(22) + a(31) + a(40) + a(23) + a(32) + a(41) + a(24) + a(33) + a(42):
s(23) = a(23) + a(32) + a(41) + a(24) + a(33) + a(42) + a(25) + a(34) + a(43):
s(24) = a(24) + a(33) + a(42) + a(25) + a(34) + a(43) + a(26) + a(35) + a(44):
s(25) = a(25) + a(34) + a(43) + a(26) + a(35) + a(44) + a(27) + a(36) + a(45):
s(26) = a(26) + a(35) + a(44) + a(27) + a(36) + a(45) + a(19) + a(28) + a(37):
s(27) = a(27) + a(36) + a(45) + a(19) + a(28) + a(37) + a(20) + a(29) + a(38):
'Clmn 4
s(28) = a(28) + a(37) + a(46) + a(29) + a(38) + a(47) + a(30) + a(39) + a(48):
s(29) = a(29) + a(38) + a(47) + a(30) + a(39) + a(48) + a(31) + a(40) + a(49):
s(30) = a(30) + a(39) + a(48) + a(31) + a(40) + a(49) + a(32) + a(41) + a(50):
s(31) = a(31) + a(40) + a(49) + a(32) + a(41) + a(50) + a(33) + a(42) + a(51):
s(32) = a(32) + a(41) + a(50) + a(33) + a(42) + a(51) + a(34) + a(43) + a(52):
s(33) = a(33) + a(42) + a(51) + a(34) + a(43) + a(52) + a(35) + a(44) + a(53):
s(34) = a(34) + a(43) + a(52) + a(35) + a(44) + a(53) + a(36) + a(45) + a(54):
s(35) = a(35) + a(44) + a(53) + a(36) + a(45) + a(54) + a(28) + a(37) + a(46):
s(36) = a(36) + a(45) + a(54) + a(28) + a(37) + a(46) + a(29) + a(38) + a(47):
'Clmn 5
s(37) = a(37) + a(46) + a(55) + a(38) + a(47) + a(56) + a(39) + a(48) + a(57):
s(38) = a(38) + a(47) + a(56) + a(39) + a(48) + a(57) + a(40) + a(49) + a(58):
s(39) = a(39) + a(48) + a(57) + a(40) + a(49) + a(58) + a(41) + a(50) + a(59):
s(40) = a(40) + a(49) + a(58) + a(41) + a(50) + a(59) + a(42) + a(51) + a(60):
s(41) = a(41) + a(50) + a(59) + a(42) + a(51) + a(60) + a(43) + a(52) + a(61):
s(42) = a(42) + a(51) + a(60) + a(43) + a(52) + a(61) + a(44) + a(53) + a(62):
s(43) = a(43) + a(52) + a(61) + a(44) + a(53) + a(62) + a(45) + a(54) + a(63):
s(44) = a(44) + a(53) + a(62) + a(45) + a(54) + a(63) + a(37) + a(46) + a(55):
s(45) = a(45) + a(54) + a(63) + a(37) + a(46) + a(55) + a(38) + a(47) + a(56):
'Clmn 6
s(46) = a(46) + a(55) + a(64) + a(47) + a(56) + a(65) + a(48) + a(57) + a(66):
s(47) = a(47) + a(56) + a(65) + a(48) + a(57) + a(66) + a(49) + a(58) + a(67):
s(48) = a(48) + a(57) + a(66) + a(49) + a(58) + a(67) + a(50) + a(59) + a(68):
s(49) = a(49) + a(58) + a(67) + a(50) + a(59) + a(68) + a(51) + a(60) + a(69):
s(50) = a(50) + a(59) + a(68) + a(51) + a(60) + a(69) + a(52) + a(61) + a(70):
s(51) = a(51) + a(60) + a(69) + a(52) + a(61) + a(70) + a(53) + a(62) + a(71):
s(52) = a(52) + a(61) + a(70) + a(53) + a(62) + a(71) + a(54) + a(63) + a(72):
s(53) = a(53) + a(62) + a(71) + a(54) + a(63) + a(72) + a(46) + a(55) + a(64):
s(54) = a(54) + a(63) + a(72) + a(46) + a(55) + a(64) + a(47) + a(56) + a(65):
'Clmn 7
s(55) = a(55) + a(64) + a(73) + a(56) + a(65) + a(74) + a(57) + a(66) + a(75):
s(56) = a(56) + a(65) + a(74) + a(57) + a(66) + a(75) + a(58) + a(67) + a(76):
s(57) = a(57) + a(66) + a(75) + a(58) + a(67) + a(76) + a(59) + a(68) + a(77):
s(58) = a(58) + a(67) + a(76) + a(59) + a(68) + a(77) + a(60) + a(69) + a(78):
s(59) = a(59) + a(68) + a(77) + a(60) + a(69) + a(78) + a(61) + a(70) + a(79):
s(60) = a(60) + a(69) + a(78) + a(61) + a(70) + a(79) + a(62) + a(71) + a(80):
s(61) = a(61) + a(70) + a(79) + a(62) + a(71) + a(80) + a(63) + a(72) + a(81):
s(62) = a(62) + a(71) + a(80) + a(63) + a(72) + a(81) + a(55) + a(64) + a(73):
s(63) = a(63) + a(72) + a(81) + a(55) + a(64) + a(73) + a(56) + a(65) + a(74):
'Clmn 8
s(64) = a(64) + a(73) + a(1) + a(65) + a(74) + a(2) + a(66) + a(75) + a(3):
s(65) = a(65) + a(74) + a(2) + a(66) + a(75) + a(3) + a(67) + a(76) + a(4):
s(66) = a(66) + a(75) + a(3) + a(67) + a(76) + a(4) + a(68) + a(77) + a(5):
s(67) = a(67) + a(76) + a(4) + a(68) + a(77) + a(5) + a(69) + a(78) + a(6):
s(68) = a(68) + a(77) + a(5) + a(69) + a(78) + a(6) + a(70) + a(79) + a(7):
s(69) = a(69) + a(78) + a(6) + a(70) + a(79) + a(7) + a(71) + a(80) + a(8):
s(70) = a(70) + a(79) + a(7) + a(71) + a(80) + a(8) + a(72) + a(81) + a(9):
s(71) = a(71) + a(80) + a(8) + a(72) + a(81) + a(9) + a(64) + a(73) + a(1):
s(72) = a(72) + a(81) + a(9) + a(64) + a(73) + a(1) + a(65) + a(74) + a(2):
'Clmn 9
s(73) = a(73) + a(1) + a(10) + a(74) + a(2) + a(11) + a(75) + a(3) + a(12):
s(74) = a(74) + a(2) + a(11) + a(75) + a(3) + a(12) + a(76) + a(4) + a(13):
s(75) = a(75) + a(3) + a(12) + a(76) + a(4) + a(13) + a(77) + a(5) + a(14):
s(76) = a(76) + a(4) + a(13) + a(77) + a(5) + a(14) + a(78) + a(6) + a(15):
s(77) = a(77) + a(5) + a(14) + a(78) + a(6) + a(15) + a(79) + a(7) + a(16):
s(78) = a(78) + a(6) + a(15) + a(79) + a(7) + a(16) + a(80) + a(8) + a(17):
s(79) = a(79) + a(7) + a(16) + a(80) + a(8) + a(17) + a(81) + a(9) + a(18):
s(80) = a(80) + a(8) + a(17) + a(81) + a(9) + a(18) + a(73) + a(1) + a(10):
s(81) = a(81) + a(9) + a(18) + a(73) + a(1) + a(10) + a(74) + a(2) + a(11):
For j20 = 1 To 81
If s(j20) <> s1 Then fl1 = 0: Exit For
Next j20
Return
' Check Row/3 and Clmn/3
1350 fl1 = 1
' Check Row/3
s(1) = a(1) + a(2) + a(3): s(10) = a(4) + a(5) + a(6): s(19) = a(7) + a(8) + a(9)
s(2) = a(10) + a(11) + a(12): s(11) = a(13) + a(14) + a(15): s(20) = a(16) + a(17) + a(18)
s(3) = a(19) + a(20) + a(21): s(12) = a(22) + a(23) + a(24): s(21) = a(25) + a(26) + a(27)
s(4) = a(28) + a(29) + a(30): s(13) = a(31) + a(32) + a(33): s(22) = a(34) + a(35) + a(36)
s(5) = a(37) + a(38) + a(39): s(14) = a(40) + a(41) + a(42): s(23) = a(43) + a(44) + a(45)
s(6) = a(46) + a(47) + a(48): s(15) = a(49) + a(50) + a(51): s(24) = a(52) + a(53) + a(54)
s(7) = a(55) + a(56) + a(57): s(16) = a(58) + a(59) + a(60): s(25) = a(61) + a(62) + a(63)
s(8) = a(64) + a(65) + a(66): s(17) = a(67) + a(68) + a(69): s(26) = a(70) + a(71) + a(72)
s(9) = a(73) + a(74) + a(75): s(18) = a(76) + a(77) + a(78): s(27) = a(79) + a(80) + a(81)
For j20 = 1 To 27
If s(j20) <> s3 Then fl1 = 0: Return
Next j20
' Check Clmn/3
s(1) = a(1) + a(10) + a(19): s(10) = a(28) + a(37) + a(46): s(19) = a(55) + a(64) + a(73)
s(2) = a(2) + a(11) + a(20): s(11) = a(29) + a(38) + a(47): s(20) = a(56) + a(65) + a(74)
s(3) = a(3) + a(12) + a(21): s(12) = a(30) + a(39) + a(48): s(21) = a(57) + a(66) + a(75)
s(4) = a(4) + a(13) + a(22): s(13) = a(31) + a(40) + a(49): s(22) = a(58) + a(67) + a(76)
s(5) = a(5) + a(14) + a(23): s(14) = a(32) + a(41) + a(50): s(23) = a(59) + a(68) + a(77)
s(6) = a(6) + a(15) + a(24): s(15) = a(33) + a(42) + a(51): s(24) = a(60) + a(69) + a(78)
s(7) = a(7) + a(16) + a(25): s(16) = a(34) + a(43) + a(52): s(25) = a(61) + a(70) + a(79)
s(8) = a(8) + a(17) + a(26): s(17) = a(35) + a(44) + a(53): s(26) = a(62) + a(71) + a(80)
s(9) = a(9) + a(18) + a(27): s(18) = a(36) + a(45) + a(54): s(27) = a(63) + a(72) + a(81)
For j20 = 1 To 27
If s(j20) <> s3 Then fl1 = 0: Exit For
Next j20
Return
' Check Square Inlays (5 x 5)
1300 fl1 = 1
s(1) = a(21) + a(22) + a(23) + a(24) + a(25)
s(2) = a(30) + a(31) + a(32) + a(33) + a(34)
s(3) = a(39) + a(40) + a(41) + a(42) + a(43)
s(4) = a(48) + a(49) + a(50) + a(51) + a(52)
s(5) = a(57) + a(58) + a(59) + a(60) + a(61)
s(6) = a(21) + a(30) + a(39) + a(48) + a(57)
s(7) = a(22) + a(31) + a(40) + a(49) + a(58)
s(8) = a(23) + a(32) + a(41) + a(50) + a(59)
s(9) = a(24) + a(33) + a(42) + a(51) + a(60)
s(10) = a(25) + a(34) + a(43) + a(52) + a(61)
s(11) = a(21) + a(31) + a(41) + a(51) + a(61)
s(12) = a(25) + a(33) + a(41) + a(49) + a(57)
For j20 = 1 To 12
If s(j20) <> s5 Then fl1 = 0: Exit For
Next j20
Return
' Check Diamond Inlay (3 x 3)
1170 fl1 = 1
s(1) = a(23) + a(33) + a(43)
s(2) = a(31) + a(41) + a(51)
s(3) = a(39) + a(49) + a(59)
s(4) = a(39) + a(31) + a(23)
s(5) = a(49) + a(41) + a(33)
s(6) = a(59) + a(51) + a(43)
s(7) = a(39) + a(41) + a(43)
s(8) = a(23) + a(41) + a(59)
For j20 = 1 To 8
If s(j20) <> s3 Then fl1 = 0: Exit For
Next j20
Return
' Check Diamond Inlay (4 x 4)
1200 fl1 = 1
s(1) = a(14) + a(24) + a(34) + a(44)
s(2) = a(22) + a(32) + a(42) + a(52)
s(3) = a(30) + a(40) + a(50) + a(60)
s(4) = a(38) + a(48) + a(58) + a(68)
s(5) = a(38) + a(30) + a(22) + a(14)
s(6) = a(48) + a(40) + a(32) + a(24)
s(7) = a(58) + a(50) + a(42) + a(34)
s(8) = a(68) + a(60) + a(52) + a(44)
For j20 = 1 To 8
If s(j20) <> s4 Then fl1 = 0: Exit For
Next j20
Return
' Check Diamond Inlays (5 x 5)
1250 fl1 = 1
s(1) = a(37) + a(29) + a(21) + a(13) + a(5)
s(2) = a(47) + a(39) + a(31) + a(23) + a(15)
s(3) = a(57) + a(49) + a(41) + a(33) + a(25)
s(4) = a(67) + a(59) + a(51) + a(43) + a(35)
s(5) = a(77) + a(69) + a(61) + a(53) + a(45)
s(6) = a(5) + a(15) + a(25) + a(35) + a(45)
s(7) = a(13) + a(23) + a(33) + a(43) + a(53)
s(8) = a(21) + a(31) + a(41) + a(51) + a(61)
s(9) = a(29) + a(39) + a(49) + a(59) + a(69)
s(10) = a(37) + a(47) + a(57) + a(67) + a(77)
For j20 = 1 To 10
If s(j20) <> s5 Then fl1 = 0: Exit For
Next j20
Return
' Check Associated Magic Squares
1050 fl1 = 1
s(1) = a(1) + a(81): s(11) = a(11) + a(71): s(21) = a(21) + a(61): s(31) = a(31) + a(51):
s(2) = a(2) + a(80): s(12) = a(12) + a(70): s(22) = a(22) + a(60): s(32) = a(32) + a(50):
s(3) = a(3) + a(79): s(13) = a(13) + a(69): s(23) = a(23) + a(59): s(33) = a(33) + a(49):
s(4) = a(4) + a(78): s(14) = a(14) + a(68): s(24) = a(24) + a(58): s(34) = a(34) + a(48):
s(5) = a(5) + a(77): s(15) = a(15) + a(67): s(25) = a(25) + a(57): s(35) = a(35) + a(47):
s(6) = a(6) + a(76): s(16) = a(16) + a(66): s(26) = a(26) + a(56): s(36) = a(36) + a(46):
s(7) = a(7) + a(75): s(17) = a(17) + a(65): s(27) = a(27) + a(55): s(37) = a(37) + a(45):
s(8) = a(8) + a(74): s(18) = a(18) + a(64): s(28) = a(28) + a(54): s(38) = a(38) + a(44):
s(9) = a(9) + a(73): s(19) = a(19) + a(63): s(29) = a(29) + a(53): s(39) = a(39) + a(43):
s(10) = a(10) + a(72): s(20) = a(20) + a(62): s(30) = a(30) + a(52): s(40) = a(40) + a(42):
For j20 = 1 To 40
If s(j20) <> s2 Then fl1 = 0: Exit For
Next j20
Return
' Check Pan Diagonals
1100 fl1 = 1
s(1) = a(1) + a(11) + a(21) + a(31) + a(41) + a(51) + a(61) + a(71) + a(81)
s(2) = a(2) + a(12) + a(22) + a(32) + a(42) + a(52) + a(62) + a(72) + a(73)
s(3) = a(3) + a(13) + a(23) + a(33) + a(43) + a(53) + a(63) + a(64) + a(74)
s(4) = a(4) + a(14) + a(24) + a(34) + a(44) + a(54) + a(55) + a(65) + a(75)
s(5) = a(5) + a(15) + a(25) + a(35) + a(45) + a(46) + a(56) + a(66) + a(76)
s(6) = a(6) + a(16) + a(26) + a(36) + a(37) + a(47) + a(57) + a(67) + a(77)
s(7) = a(7) + a(17) + a(27) + a(28) + a(38) + a(48) + a(58) + a(68) + a(78)
s(8) = a(8) + a(18) + a(19) + a(29) + a(39) + a(49) + a(59) + a(69) + a(79)
s(9) = a(9) + a(10) + a(20) + a(30) + a(40) + a(50) + a(60) + a(70) + a(80)
s(10) = a(73) + a(65) + a(57) + a(49) + a(41) + a(33) + a(25) + a(17) + a(9)
s(11) = a(74) + a(66) + a(58) + a(50) + a(42) + a(34) + a(26) + a(18) + a(1)
s(12) = a(75) + a(67) + a(59) + a(51) + a(43) + a(35) + a(27) + a(10) + a(2)
s(13) = a(76) + a(68) + a(60) + a(52) + a(44) + a(36) + a(19) + a(11) + a(3)
s(14) = a(77) + a(69) + a(61) + a(53) + a(45) + a(28) + a(20) + a(12) + a(4)
s(15) = a(78) + a(70) + a(62) + a(54) + a(37) + a(29) + a(21) + a(13) + a(5)
s(16) = a(79) + a(71) + a(63) + a(46) + a(38) + a(30) + a(22) + a(14) + a(6)
s(17) = a(80) + a(72) + a(55) + a(47) + a(39) + a(31) + a(23) + a(15) + a(7)
s(18) = a(81) + a(64) + a(56) + a(48) + a(40) + a(32) + a(24) + a(16) + a(8)
For j20 = 1 To 18
If s(j20) <> s1 Then fl1 = 0: Exit For
Next j20
Return
' Print results (selected numbers)
2645 For i1 = 1 To 81
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 82).Value = n9
Cells(1, 83).Value = n9
Return
' Print results (squares)
2650 n2 = n2 + 1
If n2 = 5 Then
n2 = 1: k1 = k1 + 10: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 10
End If
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = n9
Cells(k1, k2 + 2).Value = j100
Cells(k1, k2 + 3).Value = j200
i3 = 0
For i1 = 1 To 9
For i2 = 1 To 9
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
End Sub
