Magic esquire 3x3

motilulla · May 12, 2018

Hello,

Is it possible to create all possible magic esquire 3x3 which total must be 14 using 0 to 8 numbers? Numbers can be used repeated

Like example shown below...

Book1

A

B

C

D

E

F

1

2

3

0

3

1

2

4

1

0

2

1

5

2

0

3

2

6

3

7

4

5

2

1

8

5

2

0

3

9

6

0

1

0

10

7

11

8

3

2

1

12

1

4

13

1

0

1

14

15

3

2

0

16

1

2

17

0

1

3

18

19

3

1

0

20

1

5

1

21

1

2

0

22

23

5

2

1

24

0

3

25

0

1

2

26

27

2

1

28

3

2

29

1

0

30

31

3

2

32

2

1

33

0

1

2

34

35

4

2

1

36

0

1

37

2

3

1

38

39

1

6

0

40

2

41

1

0

42

43

0

1

3

44

1

3

45

1

2

46

47

1

2

48

1

49

1

2

3

50

51

2

1

2

52

1

2

53

1

3

1

54

55

6

2

1

56

3

0

1

57

0

1

58

59

Sheet2

Thank you all
Excel 2000
Regards,
Moti

motilulla · May 12, 2018

Hello, Please ignore posrt#1

I think not to complicate making esquires could be made all possible set using 0 to 8 numbers, could be repeated, which line total must be 14

New example

Book1

A

B

C

D

E

F

G

H

I

J

K

L

M

N

1

2

Sum

3

0

3

1

2

0

2

1

0

3

2

14

4

1

5

2

1

2

0

3

0

1

0

14

5

2

3

2

1

4

1

0

1

14

6

3

2

0

1

2

0

1

3

14

7

4

3

1

0

1

5

1

2

0

14

8

5

2

1

0

3

0

1

2

14

9

6

2

1

3

2

1

0

14

10

7

3

2

1

0

1

2

14

11

8

4

2

1

0

1

2

3

1

14

12

1

6

0

2

1

0

14

13

0

1

3

1

3

1

2

14

1

2

1

2

3

14

15

2

1

2

1

2

1

3

1

14

16

6

2

1

3

0

1

0

1

14

17

18

19

20

21

22

23

24

25

26

27

28

Sheet3

Thank you
Regards
Moti

oldbrewer · May 12, 2018

have 9 loops all going from 0 to 8 and after each loop check total
if equal to 14 make remaining numbers zero
if greater than 14 ignore and update PREVIOUS loop

ie
for A= 0 to 8
for B=0 to 8 etc etc

motilulla · May 12, 2018

oldbrewer said:
have 9 loops all going from 0 to 8 and after each loop check total
if equal to 14 make remaining numbers zero
if greater than 14 ignore and update PREVIOUS loop

ie
for A= 0 to 8
for B=0 to 8 etc etc

Hello oldbrewer,
May be like shown below 1st set 0,0,0,0,0,0,0,6,8 & last one 8,6,0,0,0,0,0,0,0

Example.

Book1

A

B

C

D

E

F

G

H

I

J

K

L

M

N

1

2

Sum

3

0

6

8

14

4

1

0

6

0

8

14

5

2

0

6

0

8

14

6

3

0

6

0

8

14

7

4

0

6

0

8

14

8

5

0

6

0

8

14

9

6

0

6

0

8

14

10

7

6

0

8

14

11

8

0

7

14

12

0

7

0

7

14

13

0

7

0

7

14

0

7

0

7

14

15

0

7

0

7

14

16

8

6

0

14

17

18

19

20

21

22

23

24

25

26

27

28

Sheet4

Thank you
Regards
Mot

oldbrewer · May 12, 2018

yes - there will be a lot of answers......do you need them all or say just 100 ?

motilulla · May 12, 2018

oldbrewer said:
yes - there will be a lot of answers......do you need them all or say just 100 ?

Hello oldbrewer,
Do you know how much could be all? i have no idea how to calculate them

Is it possible to at have all, if not could be 100 random as you can

Thank you
Regards
Moti

shg · May 12, 2018

Code:

Sub moti()
  Const m           As Long = 9
  Dim i             As Long
  Dim n             As Long
  Dim aiInx(1 To 9) As Long
  Dim aiMin(1 To 9) As Long
  Dim aiMax(1 To 9) As Long
  Dim aiOut(1 To 308187, 1 To 9) As Long
  Dim iSum          As Long

  For i = 1 To m
    aiMax(i) = 8
  Next i

  NestedFor aiInx, aiMin, aiMax, True

  Do While NestedFor(aiInx, aiMin, aiMax)
    iSum = 0
    For i = 1 To m
      iSum = iSum + aiInx(i)
      If iSum > 14 Then Exit For
    Next i

    If iSum = 14 Then
      n = n + 1

      For i = 1 To 9
        aiOut(n, i) = aiInx(i)
      Next i

      If (n And &H3FF&) = 0& Then
        Application.StatusBar = Format(n, "#,##0")
        DoEvents
      End If
    End If
  Loop

  Range("A1").Resize(UBound(aiOut, 1), UBound(aiOut, 2)).Value = aiOut
  Application.StatusBar = False
End Sub

Function NestedFor(aiInx() As Long, aiMin() As Long, aiMax() As Long, _
                   Optional bInit As Boolean = False) As Boolean
  ' shg 2007

  ' Changes array aiInx to the next iteration, varying aiInx between the values
  ' in aiMin and aiMax. The three arrays must all be 1-based and the same size.

  ' aiInx(m) is the innermost loop

  ' To initialize aiInx so that the *next* call returns the first iteration,
  ' call with bInit True.

  ' Init returns           {aiMin(1), aiMin(2), ..., aiMin(m) - 1}
  ' The first iteration is {aiMin(1), aiMin(2), ..., aiMin(m)}
  ' The last is            {aiMax(1), aiMax(2), ..., aiMax(m)}

  ' Returns False when no more iterations exist

  Dim i             As Long
  Dim m             As Long

  m = UBound(aiInx)

  If bInit Then
    For i = 1 To m - 1
      aiInx(i) = aiMin(i)
    Next i
    aiInx(m) = aiMin(i) - 1
    NestedFor = True

  Else
    For i = m To 1 Step -1
      If aiInx(i) < aiMax(i) Then
        aiInx(i) = aiInx(i) + 1
        Exit For
      End If
      aiInx(i) = aiMin(i)
    Next i
    NestedFor = i > 0
  End If
End Function

Pretty boring parade:

[Table="width:, class:grid"][tr][td="bgcolor:#C0C0C0"][/td][td="bgcolor:#C0C0C0"]

A

[/td][td="bgcolor:#C0C0C0"]

B

[/td][td="bgcolor:#C0C0C0"]

C

[/td][td="bgcolor:#C0C0C0"]

D

[/td][td="bgcolor:#C0C0C0"]

E

[/td][td="bgcolor:#C0C0C0"]

F

[/td][td="bgcolor:#C0C0C0"]

G

[/td][td="bgcolor:#C0C0C0"]

H

[/td][td="bgcolor:#C0C0C0"]

I

[/td][/tr][tr][td="bgcolor:#C0C0C0"]

1

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

6

[/td][td]

8

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

2

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

7

[/td][td]

7

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

3

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

8

[/td][td]

6

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

4

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

5

[/td][td]

8

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

5

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

6

[/td][td]

7

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

6

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

7

[/td][td]

6

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

7

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

8

[/td][td]

5

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

8

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

2

[/td][td]

4

[/td][td]

8

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

9

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

2

[/td][td]

5

[/td][td]

7

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

10

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

2

[/td][td]

6

[/td][td]

6

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

11

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

2

[/td][td]

7

[/td][td]

5

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308179

[/td][td]

8

[/td][td]

4

[/td][td]

2

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308180

[/td][td]

8

[/td][td]

5

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308181

[/td][td]

8

[/td][td]

5

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308182

[/td][td]

8

[/td][td]

5

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

0

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308183

[/td][td]

8

[/td][td]

5

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308184

[/td][td]

8

[/td][td]

5

[/td][td]

0

[/td][td]

0

[/td][td]

1

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308185

[/td][td]

8

[/td][td]

5

[/td][td]

0

[/td][td]

1

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308186

[/td][td]

8

[/td][td]

5

[/td][td]

1

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][/tr]
[tr][td="bgcolor:#C0C0C0"]

308187

[/td][td]

8

[/td][td]

6

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][td]

0

[/td][/tr]
[/table]

motilulla · May 12, 2018

shg said:
Code:

Sub moti() Const m As Long = 9 Dim i As Long Dim n As Long Dim aiInx(1 To 9) As Long Dim aiMin(1 To 9) As Long Dim aiMax(1 To 9) As Long Dim aiOut(1 To 308187, 1 To 9) As Long Dim iSum As Long For i = 1 To m aiMax(i) = 8 Next i NestedFor aiInx, aiMin, aiMax, True Do While NestedFor(aiInx, aiMin, aiMax) iSum = 0 For i = 1 To m iSum = iSum + aiInx(i) If iSum > 14 Then Exit For Next i If iSum = 14 Then n = n + 1 For i = 1 To 9 aiOut(n, i) = aiInx(i) Next i If (n And &H3FF&) = 0& Then Application.StatusBar = Format(n, "#,##0") DoEvents End If End If Loop Range("A1").Resize(UBound(aiOut, 1), UBound(aiOut, 2)).Value = aiOut Application.StatusBar = False End Sub Function NestedFor(aiInx() As Long, aiMin() As Long, aiMax() As Long, _ Optional bInit As Boolean = False) As Boolean ' shg 2007 ' Changes array aiInx to the next iteration, varying aiInx between the values ' in aiMin and aiMax. The three arrays must all be 1-based and the same size. ' aiInx(m) is the innermost loop ' To initialize aiInx so that the *next* call returns the first iteration, ' call with bInit True. ' Init returns {aiMin(1), aiMin(2), ..., aiMin(m) - 1} ' The first iteration is {aiMin(1), aiMin(2), ..., aiMin(m)} ' The last is {aiMax(1), aiMax(2), ..., aiMax(m)} ' Returns False when no more iterations exist Dim i As Long Dim m As Long m = UBound(aiInx) If bInit Then For i = 1 To m - 1 aiInx(i) = aiMin(i) Next i aiInx(m) = aiMin(i) - 1 NestedFor = True Else For i = m To 1 Step -1 If aiInx(i) < aiMax(i) Then aiInx(i) = aiInx(i) + 1 Exit For End If aiInx(i) = aiMin(i) Next i NestedFor = i > 0 End If End Function

Pretty boring parade:

[TABLE="class: grid"]
<tbody>[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "][/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

A
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

B
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

C
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

D
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

E
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

F
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

G
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

H
[/TD]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

I
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

1
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
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0
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0
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

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7
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7
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

3
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

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5
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

8
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[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

9
[/TD]
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0
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[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

2
[/TD]
[TD]

5
[/TD]
[TD]

7
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

10
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

2
[/TD]
[TD]

6
[/TD]
[TD]

6
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

11
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

2
[/TD]
[TD]

7
[/TD]
[TD]

5
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308179
[/TD]
[TD]

8
[/TD]
[TD]

4
[/TD]
[TD]

2
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308180
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

1
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308181
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

1
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308182
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

1
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308183
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

1
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308184
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

1
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308185
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

0
[/TD]
[TD]

1
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308186
[/TD]
[TD]

8
[/TD]
[TD]

5
[/TD]
[TD]

1
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
[TR]
[TD="bgcolor: [URL=https://www.mrexcel.com/forum/usertag.php?do=list&action=hash&hash=C0C0C0]#C0C0C0[/URL] "]

308187
[/TD]
[TD]

8
[/TD]
[TD]

6
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[TD]

0
[/TD]
[/TR]
</tbody>[/TABLE]

shg, thank you so much, code seems to work but it stop at the line below, because I have max 65000 lines, may it need alteration to continue in the next columns, Please does it is possible?

Code:

 Range("A1").Resize(UBound(aiOut, 1), UBound(aiOut, 2)).Value = aiOut

Thank you
Regards
Moti

motilulla · May 13, 2018

motilulla said:
shg, thank you so much, code seems to work but it stop at the line below, because I have max 65000 lines, may it need alteration to continue in the next columns, Please does it is possible?

Code:

Range("A1").Resize(UBound(aiOut, 1), UBound(aiOut, 2)).Value = aiOut

Thank you
Regards
Moti

Hello,

Code stop at the line above and do not show any results, it is due to my version 2000 has line limits 65336, and total set are 308187, please require modification after 65000 rows continue generating in the next sheet or next columns in the same sheet.

Thank you

Regards
Moti

oldbrewer · May 13, 2018

what are you going to do with 308,187 permutations ?

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