' Constructs 10 x 10 Magic Squares with Non Overlapping Subsquares (Distinct Integers):
' - Read Symmetrical Magic Square (6 x 6)
' - Generate Magic Rectangles (4 x 6) and Pan Magic Square (4 x 4)
' Tested with Office 2007 under Windows 7
Sub Priem10c2()
Dim a1(100), a(100), b1(100), b(100), c(100)
Dim d6(36) 'Sub Square
y = MsgBox("Locked", vbCritical, "Routine Priem10c2")
End
n2 = 0: n3 = 0: k1 = 1: k2 = 1: n9 = 0
' Generate Squares
Sheets("Klad1").Select
t1 = Timer
For j100 = 102 To 201
' Start Reading Data
MC6 = Sheets("Lines6").Cells(j100, 37).Value
MC10 = 5 * MC6 / 3
' Read Integers used for PM6
For i1 = 1 To 36
d6(i1) = Sheets("Lines6").Cells(j100, i1).Value
Next i1
GoSub 2010 'Define Integers
GoSub 950 'Remove used Integers from available Integers
GoSub 600 'Store 6 x 6 Square in a()
' Generate Magic Rectangle (Right/Top)
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(5) = s6 / 3 - a(40): If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j39 = m1 To m2 'a(39)
If b1(a1(j39)) = 0 Then GoTo 390
If b(a1(j39)) = 0 Then b(a1(j39)) = a1(j39): c(39) = a1(j39) Else GoTo 390
a(39) = a1(j39)
a(6) = s6 / 3 - a(39): If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
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(7) = s6 / 3 - a(38): If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
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(8) = s6 / 3 - a(37): If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
For j36 = m1 To m2 'a(36)
If b1(a1(j36)) = 0 Then GoTo 360
If b(a1(j36)) = 0 Then b(a1(j36)) = a1(j36): c(36) = a1(j36) Else GoTo 360
a(36) = a1(j36)
a(35) = s6 - a(36) - a(37) - a(38) - a(39) - a(40)
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(10) = s6 / 3 - a(35): If b(a(10)) = 0 Then b(a(10)) = a(10): c(10) = a(10) Else GoTo 100
a(9) = s6 / 3 - a(36): If b(a(9)) = 0 Then b(a(9)) = a(9): c(9) = a(9) Else GoTo 90
For j30 = m1 To m2 'a(30)
If b1(a1(j30)) = 0 Then GoTo 300
If b(a1(j30)) = 0 Then b(a1(j30)) = a1(j30): c(30) = a1(j30) Else GoTo 300
a(30) = a1(j30)
a(15) = s6 / 3 - a(30): If b(a(15)) = 0 Then b(a(15)) = a(15): c(15) = a(15) Else GoTo 150
For j29 = m1 To m2 'a(29)
If b1(a1(j29)) = 0 Then GoTo 290
If b(a1(j29)) = 0 Then b(a1(j29)) = a1(j29): c(29) = a1(j29) Else GoTo 290
a(29) = a1(j29)
a(28) = s6 - a(29) - a(30) - a(38) - a(39) - a(40)
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(27) = s6 - a(29) - a(30) - a(37) - a(39) - a(40)
If a(27) < a1(m1) Or a(27) > a1(m2) Then GoTo 270
If b1(a(27)) = 0 Then GoTo 270
If b(a(27)) = 0 Then b(a(27)) = a(27): c(27) = a(27) Else GoTo 270
a(26) = a(29) - a(36) + a(39)
If a(26) < a1(m1) Or a(26) > a1(m2) Then GoTo 260
If b1(a(26)) = 0 Then GoTo 260
If b(a(26)) = 0 Then b(a(26)) = a(26): c(26) = a(26) Else GoTo 260
a(25) = a(30) - a(35) + a(40)
If a(25) < a1(m1) Or a(25) > a1(m2) Then GoTo 250
If b1(a(25)) = 0 Then GoTo 250
If b(a(25)) = 0 Then b(a(25)) = a(25): c(25) = a(25) Else GoTo 250
a(20) = s6 / 3 - a(25): If b(a(20)) = 0 Then b(a(20)) = a(20): c(20) = a(20) Else GoTo 200
a(19) = s6 / 3 - a(26): If b(a(19)) = 0 Then b(a(19)) = a(19): c(19) = a(19) Else GoTo 190
a(18) = s6 / 3 - a(27): If b(a(18)) = 0 Then b(a(18)) = a(18): c(18) = a(18) Else GoTo 180
a(17) = s6 / 3 - a(28): If b(a(17)) = 0 Then b(a(17)) = a(17): c(17) = a(17) Else GoTo 170
a(16) = s6 / 3 - a(29): If b(a(16)) = 0 Then b(a(16)) = a(16): c(16) = a(16) Else GoTo 160
s2 = a(55) + a(46) + a(37) + a(28) + a(19) + a(10)
' Generate Magic Rectangle (Left/Bottom)
For j91 = m1 To m2 'a(91)
If b1(a1(j91)) = 0 Then GoTo 910
If b(a1(j91)) = 0 Then b(a1(j91)) = a1(j91): c(91) = a1(j91) Else GoTo 910
a(91) = a1(j91)
a(44) = s6 / 3 - a(91): If b(a(44)) = 0 Then b(a(44)) = a(44): c(44) = a(44) Else GoTo 440
For j82 = m1 To m2 'a(82)
If b1(a1(j82)) = 0 Then GoTo 820
If b(a1(j82)) = 0 Then b(a1(j82)) = a1(j82): c(82) = a1(j82) Else GoTo 820
a(82) = a1(j82)
a(53) = s6 / 3 - a(82): If b(a(53)) = 0 Then b(a(53)) = a(53): c(53) = a(53) Else GoTo 530
For j73 = m1 To m2 'a(73)
If b1(a1(j73)) = 0 Then GoTo 730
If b(a1(j73)) = 0 Then b(a1(j73)) = a1(j73): c(73) = a1(j73) Else GoTo 730
a(73) = a1(j73)
a(64) = s10 - s2 - a(73) - a(82) - a(91)
If a(64) < a1(m1) Or a(64) > a1(m2) Then GoTo 640
If b1(a(64)) = 0 Then GoTo 640
If b(a(64)) = 0 Then b(a(64)) = a(64): c(64) = a(64) Else GoTo 640
a(62) = s6 / 3 - a(73): If b(a(62)) = 0 Then b(a(62)) = a(62): c(62) = a(62) Else GoTo 620
a(71) = s6 / 3 - a(64): If b(a(71)) = 0 Then b(a(71)) = a(71): c(71) = a(71) Else GoTo 710
For j81 = m1 To m2 'a(81)
If b1(a1(j81)) = 0 Then GoTo 810
If b(a1(j81)) = 0 Then b(a1(j81)) = a1(j81): c(81) = a1(j81) Else GoTo 810
a(81) = a1(j81)
a(54) = s6 / 3 - a(81): If b(a(54)) = 0 Then b(a(54)) = a(54): c(54) = a(54) Else GoTo 540
For j61 = m1 To m2 'a(61)
If b1(a1(j61)) = 0 Then GoTo 610
If b(a1(j61)) = 0 Then b(a1(j61)) = a1(j61): c(61) = a1(j61) Else GoTo 610
a(61) = a1(j61)
a(72) = a(61) + a(64) - a(73)
If a(72) < a1(m1) Or a(72) > a1(m2) Then GoTo 720
If b1(a(72)) = 0 Then GoTo 720
If b(a(72)) = 0 Then b(a(72)) = a(72): c(72) = a(72) Else GoTo 720
a(92) = 2 * s6 / 3 - a(61) - a(81) + a(73) - a(82) - a(91)
If a(92) < a1(m1) Or a(92) > a1(m2) Then GoTo 920
If b1(a(92)) = 0 Then GoTo 920
If b(a(92)) = 0 Then b(a(92)) = a(92): c(92) = a(92) Else GoTo 920
a(43) = s6 / 3 - a(92): If b(a(43)) = 0 Then b(a(43)) = a(43): c(43) = a(43) Else GoTo 430
a(63) = s6 / 3 - a(72): If b(a(63)) = 0 Then b(a(63)) = a(63): c(63) = a(63) Else GoTo 630
a(74) = s6 / 3 - a(61): If b(a(74)) = 0 Then b(a(74)) = a(74): c(74) = a(74) Else GoTo 740
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(41) = 2 * s6 / 3 - a(51) - a(61) - a(81) + a(64) - a(91)
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(51) - a(64) + a(73) - a(82) + a(91)
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(52) = -a(51) + a(81) + a(82)
If a(52) < a1(m1) Or a(52) > a1(m2) Then GoTo 520
If b1(a(52)) = 0 Then GoTo 520
If b(a(52)) = 0 Then b(a(52)) = a(52): c(52) = a(52) Else GoTo 520
a(83) = s6 / 3 - a(52): If b(a(83)) = 0 Then b(a(83)) = a(83): c(83) = a(83) Else GoTo 830
a(93) = s6 / 3 - a(42): If b(a(93)) = 0 Then b(a(93)) = a(93): c(93) = a(93) Else GoTo 930
a(94) = s6 / 3 - a(41): If b(a(94)) = 0 Then b(a(94)) = a(94): c(94) = a(94) Else GoTo 940
a(84) = s6 / 3 - a(51): If b(a(84)) = 0 Then b(a(84)) = a(84): c(84) = a(84) Else GoTo 840
GoSub 2000 'Generate Pan Magic Square (4 x 4)
If fl2 = 0 Then GoTo 5 'Not Possible
GoSub 1800 'Exclude solutions with identical numbers (Back Check)
If fl1 = 1 Then
' n9 = n9 + 1: GoSub 1640 'Print results (lines)
n9 = n9 + 1: GoSub 1650 'Print results (squares)
End If
Erase b, c: n10 = 0: GoTo 500 'Print only first square
5
b(c(84)) = 0: c(84) = 0
840 b(c(94)) = 0: c(94) = 0
940 b(c(93)) = 0: c(93) = 0
930 b(c(83)) = 0: c(83) = 0
830 b(c(52)) = 0: c(52) = 0
520 b(c(42)) = 0: c(42) = 0
420 b(c(41)) = 0: c(41) = 0
410 b(c(51)) = 0: c(51) = 0
510 Next j51
b(c(74)) = 0: c(74) = 0
740 b(c(63)) = 0: c(63) = 0
630 b(c(43)) = 0: c(43) = 0
430 b(c(92)) = 0: c(92) = 0
920 b(c(72)) = 0: c(72) = 0
720 b(c(61)) = 0: c(61) = 0
610 Next j61
b(c(54)) = 0: c(54) = 0
540 b(c(81)) = 0: c(81) = 0
810 Next j81
b(c(71)) = 0: c(71) = 0
710 b(c(62)) = 0: c(62) = 0
620 b(c(64)) = 0: c(64) = 0
640 b(c(73)) = 0: c(73) = 0
730 Next j73
b(c(53)) = 0: c(53) = 0
530 b(c(82)) = 0: c(82) = 0
820 Next j82
b(c(44)) = 0: c(44) = 0
440 b(c(91)) = 0: c(91) = 0
910 Next j91
' Left/Bottom Not Found
b(c(16)) = 0: c(16) = 0
160 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(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 Next j29
b(c(15)) = 0: c(15) = 0
150 b(c(30)) = 0: c(30) = 0
300 Next j30
b(c(9)) = 0: c(9) = 0
90 b(c(10)) = 0: c(10) = 0
100 b(c(35)) = 0: c(35) = 0
350 b(c(36)) = 0: c(36) = 0
360 Next j36
b(c(8)) = 0: c(8) = 0
80 b(c(37)) = 0: c(37) = 0
370 Next j37
b(c(7)) = 0: c(7) = 0
70 b(c(38)) = 0: c(38) = 0
380 Next j38
b(c(6)) = 0: c(6) = 0
60 b(c(39)) = 0: c(39) = 0
390 Next j39
b(c(5)) = 0: c(5) = 0
50 b(c(40)) = 0: c(40) = 0
400 Next j40
n10 = 0
500 Next j100
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions for sum" + Str(s10)
y = MsgBox(t10, 0, "Routine Priem10c2")
End
' Compose Main Square
600 Erase a
a(45) = d6(1): a(46) = d6(2): a(47) = d6(3): a(48) = d6(4): a(49) = d6(5): a(50) = d6(6):
a(55) = d6(7): a(56) = d6(8): a(57) = d6(9): a(58) = d6(10): a(59) = d6(11): a(60) = d6(12):
a(65) = d6(13): a(66) = d6(14): a(67) = d6(15): a(68) = d6(16): a(69) = d6(17): a(70) = d6(18):
a(75) = d6(19): a(76) = d6(20): a(77) = d6(21): a(78) = d6(22): a(79) = d6(23): a(80) = d6(24):
a(85) = d6(25): a(86) = d6(26): a(87) = d6(27): a(88) = d6(28): a(89) = d6(29): a(90) = d6(30):
a(95) = d6(31): a(96) = d6(32): a(97) = d6(33): a(98) = d6(34): a(99) = d6(35): a(100) = d6(36):
Return
' Generate Pan Magic Square (4 x 4)
2000 fl2 = 1
For j34 = m1 To m2 'a(34)
If b1(a1(j34)) = 0 Then GoTo 340
If b(a1(j34)) = 0 Then b(a1(j34)) = a1(j34): c(34) = a1(j34) Else GoTo 340
a(34) = a1(j34)
a(12) = 0.5 * s4 - a(34): If b(a(12)) = 0 Then b(a(12)) = a(12): c(12) = a(12) Else GoTo 120
For j33 = m1 To m2 'a(33)
If b1(a1(j33)) = 0 Then GoTo 330
If b(a1(j33)) = 0 Then b(a1(j33)) = a1(j33): c(33) = a1(j33) Else GoTo 330
a(33) = a1(j33)
a(11) = 0.5 * s4 - a(33): If b(a(11)) = 0 Then b(a(11)) = a(11): c(11) = a(11) Else GoTo 110
For j32 = m1 To m2 'a(32)
If b1(a1(j32)) = 0 Then GoTo 320
If b(a1(j32)) = 0 Then b(a1(j32)) = a1(j32): c(32) = a1(j32) Else GoTo 320
a(32) = a1(j32)
a(31) = s4 - a(32) - a(33) - a(34)
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(14) = 0.5 * s4 - a(32): If b(a(14)) = 0 Then b(a(14)) = a(14): c(14) = a(14) Else GoTo 140
a(13) = 0.5 * s4 - a(31): If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
For j24 = m1 To m2 'a(24)
If b1(a1(j24)) = 0 Then GoTo 240
If b(a1(j24)) = 0 Then b(a1(j24)) = a1(j24): c(24) = a1(j24) Else GoTo 240
a(24) = a1(j24)
a(23) = s4 - a(24) - a(33) - a(34)
If a(23) < a1(m1) Or a(23) > a1(m2) Then GoTo 230
If b1(a(23)) = 0 Then GoTo 230
If b(a(23)) = 0 Then b(a(23)) = a(23): c(23) = a(23) Else GoTo 230
a(22) = a(24) - a(32) + a(34)
If a(22) < a1(m1) Or a(22) > a1(m2) Then GoTo 220
If b1(a(22)) = 0 Then GoTo 220
If b(a(22)) = 0 Then b(a(22)) = a(22): c(22) = a(22) Else GoTo 220
a(21) = -a(24) + a(32) + a(33)
If a(21) < a1(m1) Or a(21) > a1(m2) Then GoTo 210
If b1(a(21)) = 0 Then GoTo 210
If b(a(21)) = 0 Then b(a(21)) = a(21): c(21) = a(21) Else GoTo 210
a(4) = 0.5 * s4 - a(22): If b(a(4)) = 0 Then b(a(4)) = a(4): c(4) = a(4) Else GoTo 40
a(3) = 0.5 * s4 - a(21): If b(a(3)) = 0 Then b(a(3)) = a(3): c(3) = a(3) Else GoTo 30
a(2) = 0.5 * s4 - a(24): If b(a(2)) = 0 Then b(a(2)) = a(2): c(2) = a(2) Else GoTo 20
a(1) = 0.5 * s4 - a(23): If b(a(1)) = 0 Then b(a(1)) = a(1): c(1) = a(1) Else GoTo 10
fl2 = 1: Return
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(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 Next j24
b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 b(c(31)) = 0: c(31) = 0
310 b(c(32)) = 0: c(32) = 0
320 Next j32
b(c(11)) = 0: c(11) = 0
110 b(c(33)) = 0: c(33) = 0
330 Next j33
b(c(12)) = 0: c(12) = 0
120 b(c(34)) = 0: c(34) = 0
340 Next j34
fl2 = 0
Return
' Exclude solutions with identical numbers a()
1800 fl1 = 1
For j1 = 1 To 100
a2 = a(j1): If a2 = 0 Then GoTo 1810
For j2 = (1 + j1) To 100
If a2 = a(j2) Then fl1 = 0: Return
Next j2
1810 Next j1
Return
' Remove used Integers from available Integers
950 For j1 = 1 To 36
b1(d6(j1)) = 0
Next j1
' Restore available Integers in a1()
n20 = 0
For j1 = 1 To a20
If b1(j1) <> 0 Then
n20 = n20 + 1
a1(n20) = b1(j1)
End If
Next j1
m1 = 1: m2 = n20
Return
' Print results (lines)
1640 Cells(n9, 100).Select
For i1 = 1 To 100
Cells(n9, i1).Value = a(i1)
Next i1
Cells(n9, 101).Value = s10
Cells(n9, 102).Value = Rcrd1
Return
' Print results (squares)
1650 n2 = n2 + 1
If n2 = 3 Then
n2 = 1: k1 = k1 + 11: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 11
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = CStr(j100)
i3 = 0
For i1 = 1 To 10
For i2 = 1 To 10
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a(i3)
Next i2
Next i1
Return
' Define Integers
2010 s4 = 202: s6 = 303: s10 = 505
nVar = 100
m1 = 1: m2 = nVar
For i1 = m1 To m2
a1(i1) = i1
Next i1
a20 = 100 'Maximum
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
Return
End Sub
