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' 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

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