' Generates Inlaid Magic Squares of order 20
' Based on Order 4 Magic Sub Squares with Different Magic Sums
' Tested with Office 2007 under Windows 7
Sub Priem20k2()
Dim a1(750), a(16), a20(400), b1(48355), b(48355), c(16)
y = MsgBox("Locked", vbCritical, "Routine Priem20k2")
End
n1 = 0: n9 = 0: n10 = 0: k1 = 1: k2 = 1
Sheets("Klad1").Select
t1 = Timer
For j200 = 2 To 1292
s20 = Sheets("Input25").Cells(j200, 52).Value
Erase a20
For j101 = 27 To 51
j100 = Sheets("Input25").Cells(j200, j101).Value
' Define variables
Cntr3 = Sheets("Pairs7").Cells(j100, 6).Value 'Mid
s1 = 4 * Cntr3
nVar1 = Sheets("Pairs7").Cells(j100, 9).Value
For i1 = 1 To nVar1
a1(i1) = Sheets("Pairs7").Cells(j100, 9 + i1).Value
Next i1
m1 = 1: m2 = nVar1
If a1(1) = 1 Then m1 = 2: m2 = m2 - 1
Erase b1
For i1 = m1 To m2
b1(a1(i1)) = a1(i1)
Next i1
' Remove Used Primes
For i1 = 1 To 400
b1(a20(i1)) = 0
Next i1
' Generate Pan Magic Squares (4 x 4)
For j16 = m1 To m2 'a(16)
If b1(a1(j16)) = 0 Then GoTo 160
If b(a1(j16)) = 0 Then b(a1(j16)) = a1(j16): c(16) = a1(j16) Else GoTo 160
a(16) = a1(j16)
a(6) = 0.5 * s1 - a(16):
If a(6) < a1(m1) Or a(6) > a1(m2) Then GoTo 60
If b1(a(6)) = 0 Then GoTo 60
If b(a(6)) = 0 Then b(a(6)) = a(6): c(6) = a(6) Else GoTo 60
For j15 = m1 To m2 'a(15)
If b1(a1(j15)) = 0 Then GoTo 150
If b(a1(j15)) = 0 Then b(a1(j15)) = a1(j15): c(15) = a1(j15) Else GoTo 150
a(15) = a1(j15)
a(5) = 0.5 * s1 - a(15):
If a(5) < a1(m1) Or a(5) > a1(m2) Then GoTo 50
If b1(a(5)) = 0 Then GoTo 50
If b(a(5)) = 0 Then b(a(5)) = a(5): c(5) = a(5) Else GoTo 50
For j14 = m1 To m2 'a(14)
If b1(a1(j14)) = 0 Then GoTo 140
If b(a1(j14)) = 0 Then b(a1(j14)) = a1(j14): c(14) = a1(j14) Else GoTo 140
a(14) = a1(j14)
a(13) = s1 - a(14) - a(15) - a(16)
If a(13) < a1(m1) Or a(13) > a1(m2) Then GoTo 130
If b1(a(13)) = 0 Then GoTo 130
If b(a(13)) = 0 Then b(a(13)) = a(13): c(13) = a(13) Else GoTo 130
a(8) = 0.5 * s1 - a(14):
If a(8) < a1(m1) Or a(8) > a1(m2) Then GoTo 80
If b1(a(8)) = 0 Then GoTo 80
If b(a(8)) = 0 Then b(a(8)) = a(8): c(8) = a(8) Else GoTo 80
a(7) = 0.5 * s1 - a(13):
If a(7) < a1(m1) Or a(7) > a1(m2) Then GoTo 70
If b1(a(7)) = 0 Then GoTo 70
If b(a(7)) = 0 Then b(a(7)) = a(7): c(7) = a(7) Else GoTo 70
For j12 = m1 To m2 'a(12)
If b1(a1(j12)) = 0 Then GoTo 120
If b(a1(j12)) = 0 Then b(a1(j12)) = a1(j12): c(12) = a1(j12) Else GoTo 120
a(12) = a1(j12)
a(11) = s1 - a(12) - a(15) - a(16)
If a(11) < a1(m1) Or a(11) > a1(m2) Then GoTo 75
If b1(a(11)) = 0 Then GoTo 75
a(10) = a(12) - a(14) + a(16)
If a(10) < a1(m1) Or a(10) > a1(m2) Then GoTo 75
If b1(a(10)) = 0 Then GoTo 75
a(9) = -a(12) + a(14) + a(15)
If a(9) < a1(m1) Or a(9) > a1(m2) Then GoTo 75
If b1(a(9)) = 0 Then GoTo 75
a(4) = 0.5 * s1 - a(10)
If a(4) < a1(m1) Or a(4) > a1(m2) Then GoTo 75:
If b1(a(4)) = 0 Then GoTo 75
a(3) = 0.5 * s1 - a(9)
If a(3) < a1(m1) Or a(3) > a1(m2) Then GoTo 75:
If b1(a(3)) = 0 Then GoTo 75
a(2) = 0.5 * s1 - a(12)
If a(2) < a1(m1) Or a(2) > a1(m2) Then GoTo 75:
If b1(a(2)) = 0 Then GoTo 75
a(1) = 0.5 * s1 - a(11)
If a(1) < a1(m1) Or a(1) > a1(m2) Then GoTo 75:
If b1(a(1)) = 0 Then GoTo 75
' Exclude solutions with identical numbers
GoSub 800: If fl1 = 0 Then GoTo 75
n10 = n10 + 1: GoSub 750 'Assign to a20()
Erase b, c: GoTo 5 'Assign only first square
75 b(c(12)) = 0: c(12) = 0
120 Next j12
b(c(7)) = 0: c(7) = 0
70 b(c(8)) = 0: c(8) = 0
80 b(c(13)) = 0: c(13) = 0
130 b(c(14)) = 0: c(14) = 0
140 Next j14
b(c(5)) = 0: c(5) = 0
50 b(c(15)) = 0: c(15) = 0
150 Next j15
b(c(6)) = 0: c(6) = 0
60 b(c(16)) = 0: c(16) = 0
160 Next j16
' Not found
Erase b, c: n10 = 0: GoTo 2000
5
If n10 = 25 Then
GoSub 850:
If fl1 = 1 Then
n9 = n9 + 1: GoSub 660 'Print results (squares)
n10 = 0: GoTo 2000
End If
End If
Next j101
2000 n10 = 0
Next j200
t2 = Timer
t10 = Str(t2 - t1) + " sec., " + Str(n9) + " Solutions"
y = MsgBox(t10, 0, "Routine Priem20k2")
End
' Assign to a20()
750 Select Case n10
Case 1
a20(1) = a(1): a20(2) = a(2): a20(3) = a(3): a20(4) = a(4):
a20(21) = a(5): a20(22) = a(6): a20(23) = a(7): a20(24) = a(8):
a20(41) = a(9): a20(42) = a(10): a20(43) = a(11): a20(44) = a(12):
a20(61) = a(13): a20(62) = a(14): a20(63) = a(15): a20(64) = a(16):
Case 2
a20(5) = a(1): a20(6) = a(2): a20(7) = a(3): a20(8) = a(4):
a20(25) = a(5): a20(26) = a(6): a20(27) = a(7): a20(28) = a(8):
a20(45) = a(9): a20(46) = a(10): a20(47) = a(11): a20(48) = a(12):
a20(65) = a(13): a20(66) = a(14): a20(67) = a(15): a20(68) = a(16):
Case 3
a20(9) = a(1): a20(10) = a(2): a20(11) = a(3): a20(12) = a(4):
a20(29) = a(5): a20(30) = a(6): a20(31) = a(7): a20(32) = a(8):
a20(49) = a(9): a20(50) = a(10): a20(51) = a(11): a20(52) = a(12):
a20(69) = a(13): a20(70) = a(14): a20(71) = a(15): a20(72) = a(16):
Case 4
a20(13) = a(1): a20(14) = a(2): a20(15) = a(3): a20(16) = a(4):
a20(33) = a(5): a20(34) = a(6): a20(35) = a(7): a20(36) = a(8):
a20(53) = a(9): a20(54) = a(10): a20(55) = a(11): a20(56) = a(12):
a20(73) = a(13): a20(74) = a(14): a20(75) = a(15): a20(76) = a(16):
Case 5
a20(17) = a(1): a20(18) = a(2): a20(19) = a(3): a20(20) = a(4):
a20(37) = a(5): a20(38) = a(6): a20(39) = a(7): a20(40) = a(8):
a20(57) = a(9): a20(58) = a(10): a20(59) = a(11): a20(60) = a(12):
a20(77) = a(13): a20(78) = a(14): a20(79) = a(15): a20(80) = a(16):
Case 6
a20(81) = a(1): a20(82) = a(2): a20(83) = a(3): a20(84) = a(4):
a20(101) = a(5): a20(102) = a(6): a20(103) = a(7): a20(104) = a(8):
a20(121) = a(9): a20(122) = a(10): a20(123) = a(11): a20(124) = a(12):
a20(141) = a(13): a20(142) = a(14): a20(143) = a(15): a20(144) = a(16):
Case 7
a20(85) = a(1): a20(86) = a(2): a20(87) = a(3): a20(88) = a(4):
a20(105) = a(5): a20(106) = a(6): a20(107) = a(7): a20(108) = a(8):
a20(125) = a(9): a20(126) = a(10): a20(127) = a(11): a20(128) = a(12):
a20(145) = a(13): a20(146) = a(14): a20(147) = a(15): a20(148) = a(16):
Case 8
a20(89) = a(1): a20(90) = a(2): a20(91) = a(3): a20(92) = a(4):
a20(109) = a(5): a20(110) = a(6): a20(111) = a(7): a20(112) = a(8):
a20(129) = a(9): a20(130) = a(10): a20(131) = a(11): a20(132) = a(12):
a20(149) = a(13): a20(150) = a(14): a20(151) = a(15): a20(152) = a(16):
Case 9
a20(93) = a(1): a20(94) = a(2): a20(95) = a(3): a20(96) = a(4):
a20(113) = a(5): a20(114) = a(6): a20(115) = a(7): a20(116) = a(8):
a20(133) = a(9): a20(134) = a(10): a20(135) = a(11): a20(136) = a(12):
a20(153) = a(13): a20(154) = a(14): a20(155) = a(15): a20(156) = a(16):
Case 10
a20(97) = a(1): a20(98) = a(2): a20(99) = a(3): a20(100) = a(4):
a20(117) = a(5): a20(118) = a(6): a20(119) = a(7): a20(120) = a(8):
a20(137) = a(9): a20(138) = a(10): a20(139) = a(11): a20(140) = a(12):
a20(157) = a(13): a20(158) = a(14): a20(159) = a(15): a20(160) = a(16):
Case 11
a20(161) = a(1): a20(162) = a(2): a20(163) = a(3): a20(164) = a(4):
a20(181) = a(5): a20(182) = a(6): a20(183) = a(7): a20(184) = a(8):
a20(201) = a(9): a20(202) = a(10): a20(203) = a(11): a20(204) = a(12):
a20(221) = a(13): a20(222) = a(14): a20(223) = a(15): a20(224) = a(16):
Case 12
a20(165) = a(1): a20(166) = a(2): a20(167) = a(3): a20(168) = a(4):
a20(185) = a(5): a20(186) = a(6): a20(187) = a(7): a20(188) = a(8):
a20(205) = a(9): a20(206) = a(10): a20(207) = a(11): a20(208) = a(12):
a20(225) = a(13): a20(226) = a(14): a20(227) = a(15): a20(228) = a(16):
Case 13
a20(169) = a(1): a20(170) = a(2): a20(171) = a(3): a20(172) = a(4):
a20(189) = a(5): a20(190) = a(6): a20(191) = a(7): a20(192) = a(8):
a20(209) = a(9): a20(210) = a(10): a20(211) = a(11): a20(212) = a(12):
a20(229) = a(13): a20(230) = a(14): a20(231) = a(15): a20(232) = a(16):
Case 14
a20(173) = a(1): a20(174) = a(2): a20(175) = a(3): a20(176) = a(4):
a20(193) = a(5): a20(194) = a(6): a20(195) = a(7): a20(196) = a(8):
a20(213) = a(9): a20(214) = a(10): a20(215) = a(11): a20(216) = a(12):
a20(233) = a(13): a20(234) = a(14): a20(235) = a(15): a20(236) = a(16):
Case 15
a20(177) = a(1): a20(178) = a(2): a20(179) = a(3): a20(180) = a(4):
a20(197) = a(5): a20(198) = a(6): a20(199) = a(7): a20(200) = a(8):
a20(217) = a(9): a20(218) = a(10): a20(219) = a(11): a20(220) = a(12):
a20(237) = a(13): a20(238) = a(14): a20(239) = a(15): a20(240) = a(16):
Case 16
a20(241) = a(1): a20(242) = a(2): a20(243) = a(3): a20(244) = a(4):
a20(261) = a(5): a20(262) = a(6): a20(263) = a(7): a20(264) = a(8):
a20(281) = a(9): a20(282) = a(10): a20(283) = a(11): a20(284) = a(12):
a20(301) = a(13): a20(302) = a(14): a20(303) = a(15): a20(304) = a(16):
Case 17
a20(245) = a(1): a20(246) = a(2): a20(247) = a(3): a20(248) = a(4):
a20(265) = a(5): a20(266) = a(6): a20(267) = a(7): a20(268) = a(8):
a20(285) = a(9): a20(286) = a(10): a20(287) = a(11): a20(288) = a(12):
a20(305) = a(13): a20(306) = a(14): a20(307) = a(15): a20(308) = a(16):
Case 18
a20(249) = a(1): a20(250) = a(2): a20(251) = a(3): a20(252) = a(4):
a20(269) = a(5): a20(270) = a(6): a20(271) = a(7): a20(272) = a(8):
a20(289) = a(9): a20(290) = a(10): a20(291) = a(11): a20(292) = a(12):
a20(309) = a(13): a20(310) = a(14): a20(311) = a(15): a20(312) = a(16):
Case 19
a20(253) = a(1): a20(254) = a(2): a20(255) = a(3): a20(256) = a(4):
a20(273) = a(5): a20(274) = a(6): a20(275) = a(7): a20(276) = a(8):
a20(293) = a(9): a20(294) = a(10): a20(295) = a(11): a20(296) = a(12):
a20(313) = a(13): a20(314) = a(14): a20(315) = a(15): a20(316) = a(16):
Case 20
a20(257) = a(1): a20(258) = a(2): a20(259) = a(3): a20(260) = a(4):
a20(277) = a(5): a20(278) = a(6): a20(279) = a(7): a20(280) = a(8):
a20(297) = a(9): a20(298) = a(10): a20(299) = a(11): a20(300) = a(12):
a20(317) = a(13): a20(318) = a(14): a20(319) = a(15): a20(320) = a(16):
Case 21
a20(321) = a(1): a20(322) = a(2): a20(323) = a(3): a20(324) = a(4):
a20(341) = a(5): a20(342) = a(6): a20(343) = a(7): a20(344) = a(8):
a20(361) = a(9): a20(362) = a(10): a20(363) = a(11): a20(364) = a(12):
a20(381) = a(13): a20(382) = a(14): a20(383) = a(15): a20(384) = a(16):
Case 22
a20(325) = a(1): a20(326) = a(2): a20(327) = a(3): a20(328) = a(4):
a20(345) = a(5): a20(346) = a(6): a20(347) = a(7): a20(348) = a(8):
a20(365) = a(9): a20(366) = a(10): a20(367) = a(11): a20(368) = a(12):
a20(385) = a(13): a20(386) = a(14): a20(387) = a(15): a20(388) = a(16):
Case 23
a20(329) = a(1): a20(330) = a(2): a20(331) = a(3): a20(332) = a(4):
a20(349) = a(5): a20(350) = a(6): a20(351) = a(7): a20(352) = a(8):
a20(369) = a(9): a20(370) = a(10): a20(371) = a(11): a20(372) = a(12):
a20(389) = a(13): a20(390) = a(14): a20(391) = a(15): a20(392) = a(16):
Case 24
a20(333) = a(1): a20(334) = a(2): a20(335) = a(3): a20(336) = a(4):
a20(353) = a(5): a20(354) = a(6): a20(355) = a(7): a20(356) = a(8):
a20(373) = a(9): a20(374) = a(10): a20(375) = a(11): a20(376) = a(12):
a20(393) = a(13): a20(394) = a(14): a20(395) = a(15): a20(396) = a(16):
Case 25
a20(337) = a(1): a20(338) = a(2): a20(339) = a(3): a20(340) = a(4):
a20(357) = a(5): a20(358) = a(6): a20(359) = a(7): a20(360) = a(8):
a20(377) = a(9): a20(378) = a(10): a20(379) = a(11): a20(380) = a(12):
a20(397) = a(13): a20(398) = a(14): a20(399) = a(15): a20(400) = a(16):
End Select
Return
' Print results: squares a15()
660 n1 = n1 + 1
If n1 = 2 Then
n1 = 1: k1 = k1 + 21: k2 = 1
Else
If n9 > 1 Then k2 = k2 + 21
End If
Cells(k1, k2 + 1).Select
Cells(k1, k2 + 1).Font.Color = -4165632
Cells(k1, k2 + 1).Value = s20
i3 = 0
For i1 = 1 To 20
For i2 = 1 To 20
i3 = i3 + 1
Cells(k1 + i1, k2 + i2).Value = a20(i3)
Next i2
Next i1
Return
' Exclude solutions with identical numbers a()
800 fl1 = 1
For j1 = 1 To 16
a2 = a(j1)
For j2 = (1 + j1) To 16
If a2 = a(j2) Then fl1 = 0: Return
Next j2
Next j1
Return
' Exclude solutions with identical numbers a20()
850 fl1 = 1
For j1 = 1 To 400
a2 = a20(j1): If a2 = 0 Then GoTo 860
For j2 = (1 + j1) To 400
If a2 = a20(j2) Then fl1 = 0: Return
Next j2
860 Next j1
Return
End Sub
