Hi everyone,

I am trying to create a "Gaps" program that cycles through ALL
13,983,816 combinations in a 6 from 49 Lotto and produces the
following data.
I would like it to work out the Gaps between each of the balls for
EACH combination in a 6 from 49 Lotto with no replacement.
For example, the combination 02 08 18 28 36 45 will have the Gaps
of ...

Ball 1 numbered 02 & Ball 2 numbered 08 = 05 Gaps ( 03 04
05 06 07 )
Ball 2 numbered 08 & Ball 3 numbered 18 = 09 Gaps ( 19 10
11 12 13 14 15 16 17 )
Ball 3 numbered 18 & Ball 4 numbered 28 = 08 Gaps ( 20 21
22 23 24 25 26 27 )
Ball 4 numbered 28 & Ball 5 numbered 36 = 07 Gaps ( 29 30
31 32 33 34 35 )
Ball 5 numbered 36 & Ball 6 numbered 45 = 08 Gaps ( 37 38
39 40 41 42 43 44 )

.... so the Gaps description for this particular combination will be 05
09 08 07 08.

The Gaps difference between ball 1 and ball 2 is really ball 2 minus
ball 1 - 1 and so on.
I would like to have a Gaps description for each category and the
Total combinations for each category associated with that list.
So extracting three combinations from the Loop as an example ...

Combination - 02 09 16 25 38 45
Combination - 04 15 19 36 37 49
Combination - 09 15 28 39 46 47

.... will give the answer ...

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )
Gaps 10 03 16 00 11 = x combinations ( x could be 236,258 combinations
with the exact same Gaps between the balls 1-2, 2-3, 3-4, 4-5 & 5-6 )
Gaps 05 12 10 06 00 = x combinations ( x could be 756,258 combinations
with the exact same Gaps between the balls 1-2, 2-3, 3-4, 4-5 & 5-6 )

.... etc.

It would also be nice to have a Total at the bottom of the
combinations list, which of course, should equal 13,983,816
combinations.

I have written the following which has nothing to do with what I am
trying to achieve above, but for some reason it does not work.
It is supposed to give me a list of Gaps from 00 to 43 from ALL
13,983,816 combinations.
The list of Gaps should be in cells B3:B45 and the total combinatios
for each gap should be in cells C3:C45.
Could somebody please have a glance at it.

Option Explicit
Option Base 1

Private Sub Gaps()

Dim A As Integer
Dim B As Integer
Dim C As Integer
Dim D As Integer
Dim E As Integer
Dim F As Integer
Dim i As Integer
Dim GapsTotal(43) As Long

Application.ScreenUpdating = False

For i = 1 To 43
GapsTotal(i) = 0
Next i

For A = 1 To 44
For B = A + 1 To 45
For C = B + 1 To 46
For D = C + 1 To 47
For E = D + 1 To 48
For F = E + 1 To 49

If B - A - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If C - B - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If D - C - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If E - D - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If F - E - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1

If B - A - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If C - B - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If D - C - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If E - D - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If F - E - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1

.... continued all the way down to ...

If B - A - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If C - B - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If D - C - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If E - D - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If F - E - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1

If B - A - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If C - B - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If D - C - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If E - D - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If F - E - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1

Next F
Next E
Next D
Next C
Next B
Next A

Sheets("Gaps Data").Select

Range("B2").Value = "Gaps"
Range("B3").Value = "Gaps of 00"
Range("B4").Value = "Gaps of 01"

.... continued all the way down to ...

Range("B44").Value = "Gaps of 42"
Range("B45").Value = "Gaps of 43"

Range("C2").Value = "Total"
Range("C3").Select

For i = 1 To 43
ActiveCell.Offset(i, 0).Value = GapsTotal(i)
Next i

Application.ScreenUpdating = True
End Sub

Any help will be greatly appreciated.
Thanks in Advance.
All the Best.
Paul

I'm confused, and don't see how you get this:

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Those 'gaps' can only be produced by 6 different combinations:
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

In general, the number of combinations for any gap combinations would be 49 - SUM(Gaps) - 5
For the example above, 49 - 38 - 5 = 6 combinations

There will be lots of combinations of gaps that can only be produced by one combination. For
example:

Gaps 01 01 01 01 01 39

would be uniquely 01 03 05 07 09 49


HTH,
Bernie
MS Excel MVP


"Paul Black" wrote in message
oups.com...
Hi everyone,

I am trying to create a "Gaps" program that cycles through ALL
13,983,816 combinations in a 6 from 49 Lotto and produces the
following data.
I would like it to work out the Gaps between each of the balls for
EACH combination in a 6 from 49 Lotto with no replacement.
For example, the combination 02 08 18 28 36 45 will have the Gaps
of ...

Ball 1 numbered 02 & Ball 2 numbered 08 = 05 Gaps ( 03 04
05 06 07 )
Ball 2 numbered 08 & Ball 3 numbered 18 = 09 Gaps ( 19 10
11 12 13 14 15 16 17 )
Ball 3 numbered 18 & Ball 4 numbered 28 = 08 Gaps ( 20 21
22 23 24 25 26 27 )
Ball 4 numbered 28 & Ball 5 numbered 36 = 07 Gaps ( 29 30
31 32 33 34 35 )
Ball 5 numbered 36 & Ball 6 numbered 45 = 08 Gaps ( 37 38
39 40 41 42 43 44 )

... so the Gaps description for this particular combination will be 05
09 08 07 08.

The Gaps difference between ball 1 and ball 2 is really ball 2 minus
ball 1 - 1 and so on.
I would like to have a Gaps description for each category and the
Total combinations for each category associated with that list.
So extracting three combinations from the Loop as an example ...

Combination - 02 09 16 25 38 45
Combination - 04 15 19 36 37 49
Combination - 09 15 28 39 46 47

... will give the answer ...

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )
Gaps 10 03 16 00 11 = x combinations ( x could be 236,258 combinations
with the exact same Gaps between the balls 1-2, 2-3, 3-4, 4-5 & 5-6 )
Gaps 05 12 10 06 00 = x combinations ( x could be 756,258 combinations
with the exact same Gaps between the balls 1-2, 2-3, 3-4, 4-5 & 5-6 )

... etc.

It would also be nice to have a Total at the bottom of the
combinations list, which of course, should equal 13,983,816
combinations.

I have written the following which has nothing to do with what I am
trying to achieve above, but for some reason it does not work.
It is supposed to give me a list of Gaps from 00 to 43 from ALL
13,983,816 combinations.
The list of Gaps should be in cells B3:B45 and the total combinatios
for each gap should be in cells C3:C45.
Could somebody please have a glance at it.

Option Explicit
Option Base 1

Private Sub Gaps()

Dim A As Integer
Dim B As Integer
Dim C As Integer
Dim D As Integer
Dim E As Integer
Dim F As Integer
Dim i As Integer
Dim GapsTotal(43) As Long

Application.ScreenUpdating = False

For i = 1 To 43
GapsTotal(i) = 0
Next i

For A = 1 To 44
For B = A + 1 To 45
For C = B + 1 To 46
For D = C + 1 To 47
For E = D + 1 To 48
For F = E + 1 To 49

If B - A - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If C - B - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If D - C - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If E - D - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If F - E - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1

If B - A - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If C - B - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If D - C - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If E - D - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If F - E - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1

... continued all the way down to ...

If B - A - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If C - B - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If D - C - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If E - D - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If F - E - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1

If B - A - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If C - B - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If D - C - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If E - D - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If F - E - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1

Next F
Next E
Next D
Next C
Next B
Next A

Sheets("Gaps Data").Select

Range("B2").Value = "Gaps"
Range("B3").Value = "Gaps of 00"
Range("B4").Value = "Gaps of 01"

... continued all the way down to ...

Range("B44").Value = "Gaps of 42"
Range("B45").Value = "Gaps of 43"

Range("C2").Value = "Total"
Range("C3").Select

For i = 1 To 43
ActiveCell.Offset(i, 0).Value = GapsTotal(i)
Next i

Application.ScreenUpdating = True
End Sub

Any help will be greatly appreciated.
Thanks in Advance.
All the Best.
Paul

Bernie:

01 08 15 24 37 44

the numbers with X's represent the GAPS the number of numbers in the GAPS
make up the pattern 06 06 08 12 06. You could repeat this pattern a total
of 6 times until you ran out of numbers.

1
2x
3x
4x 6
5x
6x
7x
8
9x
10x
11x
12x 6
13x
14x
15
16x
17x
18x
19x
20x 8
21x
22x
23x
24
25x
26x
27x
28x
29x
30x 12
31x
32x
33x
34x
35x
36x
37
38x
39x
40x 6
41x
42x
43x
44
45
46
47
48
49

--
Regards,
Tom Ogilvy


"Bernie Deitrick" wrote:

I'm confused, and don't see how you get this:

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Those 'gaps' can only be produced by 6 different combinations:
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

In general, the number of combinations for any gap combinations would be 49 - SUM(Gaps) - 5
For the example above, 49 - 38 - 5 = 6 combinations

There will be lots of combinations of gaps that can only be produced by one combination. For
example:

Gaps 01 01 01 01 01 39

would be uniquely 01 03 05 07 09 49


HTH,
Bernie
MS Excel MVP


"Paul Black" wrote in message
oups.com...
Hi everyone,

I am trying to create a "Gaps" program that cycles through ALL
13,983,816 combinations in a 6 from 49 Lotto and produces the
following data.
I would like it to work out the Gaps between each of the balls for
EACH combination in a 6 from 49 Lotto with no replacement.
For example, the combination 02 08 18 28 36 45 will have the Gaps
of ...

Ball 1 numbered 02 & Ball 2 numbered 08 = 05 Gaps ( 03 04
05 06 07 )
Ball 2 numbered 08 & Ball 3 numbered 18 = 09 Gaps ( 19 10
11 12 13 14 15 16 17 )
Ball 3 numbered 18 & Ball 4 numbered 28 = 08 Gaps ( 20 21
22 23 24 25 26 27 )
Ball 4 numbered 28 & Ball 5 numbered 36 = 07 Gaps ( 29 30
31 32 33 34 35 )
Ball 5 numbered 36 & Ball 6 numbered 45 = 08 Gaps ( 37 38
39 40 41 42 43 44 )

... so the Gaps description for this particular combination will be 05
09 08 07 08.

The Gaps difference between ball 1 and ball 2 is really ball 2 minus
ball 1 - 1 and so on.
I would like to have a Gaps description for each category and the
Total combinations for each category associated with that list.
So extracting three combinations from the Loop as an example ...

Combination - 02 09 16 25 38 45
Combination - 04 15 19 36 37 49
Combination - 09 15 28 39 46 47

... will give the answer ...

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )
Gaps 10 03 16 00 11 = x combinations ( x could be 236,258 combinations
with the exact same Gaps between the balls 1-2, 2-3, 3-4, 4-5 & 5-6 )
Gaps 05 12 10 06 00 = x combinations ( x could be 756,258 combinations
with the exact same Gaps between the balls 1-2, 2-3, 3-4, 4-5 & 5-6 )

... etc.

It would also be nice to have a Total at the bottom of the
combinations list, which of course, should equal 13,983,816
combinations.

I have written the following which has nothing to do with what I am
trying to achieve above, but for some reason it does not work.
It is supposed to give me a list of Gaps from 00 to 43 from ALL
13,983,816 combinations.
The list of Gaps should be in cells B3:B45 and the total combinatios
for each gap should be in cells C3:C45.
Could somebody please have a glance at it.

Option Explicit
Option Base 1

Private Sub Gaps()

Dim A As Integer
Dim B As Integer
Dim C As Integer
Dim D As Integer
Dim E As Integer
Dim F As Integer
Dim i As Integer
Dim GapsTotal(43) As Long

Application.ScreenUpdating = False

For i = 1 To 43
GapsTotal(i) = 0
Next i

For A = 1 To 44
For B = A + 1 To 45
For C = B + 1 To 46
For D = C + 1 To 47
For E = D + 1 To 48
For F = E + 1 To 49

If B - A - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If C - B - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If D - C - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If E - D - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1
If F - E - 1 = 0 Then GapsTotal(0) = GapsTotal(0) + 1

If B - A - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If C - B - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If D - C - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If E - D - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1
If F - E - 1 = 1 Then GapsTotal(1) = GapsTotal(1) + 1

... continued all the way down to ...

If B - A - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If C - B - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If D - C - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If E - D - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1
If F - E - 1 = 42 Then GapsTotal(42) = GapsTotal(42) + 1

If B - A - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If C - B - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If D - C - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If E - D - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1
If F - E - 1 = 43 Then GapsTotal(43) = GapsTotal(43) + 1

Next F
Next E
Next D
Next C
Next B
Next A

Sheets("Gaps Data").Select

Range("B2").Value = "Gaps"
Range("B3").Value = "Gaps of 00"
Range("B4").Value = "Gaps of 01"

... continued all the way down to ...

Range("B44").Value = "Gaps of 42"
Range("B45").Value = "Gaps of 43"

Range("C2").Value = "Total"
Range("C3").Select

For i = 1 To 43
ActiveCell.Offset(i, 0).Value = GapsTotal(i)
Next i

Application.ScreenUpdating = True
End Sub

Any help will be greatly appreciated.
Thanks in Advance.
All the Best.
Paul

Tom,

You could repeat this pattern a total
of 6 times until you ran out of numbers.

I think we're in agreement:

Those 'gaps' can only be produced by 6 different combinations:
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

But I have no idea how the OP got 925,365 combinations:

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Bernie

Whoops!
mistook your explantion for part of your question <face red. Have to
confess I didn't read the original post so thought it was all a quote.

--
Regards,
Tom Ogilvy


"Bernie Deitrick" wrote:


Tom,

You could repeat this pattern a total
of 6 times until you ran out of numbers.

I think we're in agreement:

Those 'gaps' can only be produced by 6 different combinations:
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

But I have no idea how the OP got 925,365 combinations:

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Bernie

Thanks for the code Bernie.

I don't have access to Excel at the moment so am unable to test the
code.
Does the code apply to my original request or to my Private Sub Gaps()
effort please. I assume it applies to my effort.
It is my original request that is the most important one.

Thanks in Advance.
All the Best.
Paul

On Jul 10, 5:04 pm, Tom Ogilvy
wrote:
Whoops!
mistook your explantion for part of your question <face red. Have to
confess I didn't read the original post so thought it was all a quote.

--
Regards,
Tom Ogilvy



"Bernie Deitrick" wrote:

Tom,

You could repeat this pattern a total
of 6 times until you ran out of numbers.

I think we're in agreement:

Those 'gaps' can only be produced by 6 different combinations:
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

But I have no idea how the OP got 925,365 combinations:

Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Bernie- Hide quoted text -

- Show quoted text -

Thanks for the reply Bernie,

The Gaps 06 06 08 12 06 = x combinations ( x could be 925,365
combinations with the exact same Gaps between the balls 1 & 2, and 2 &
3, and 3 & 4, and 4 & 5, and 5 & 6 ) is only an example figure, I have
no idea what the actual figure is, or come to it, how to code it.

There can only be 5 criteria for each combination. These are the gaps
between balls ...
1 and 2
2 and 3
3 and 4
4 and 5
5 and 6
.... obviously with ALL 13,983,816 combinations there will be quite a
few categories.
The Gaps are produced for each category using all the 6 numbers within
each combination.

Begin Quote :-
Gaps 01 01 01 01 01 39 ( how did you get the 6 sets of
numbers? ) ...
.... would be uniquely 01 03 05 07 09 49
End Quote.

I don't quite understand it when you say ...

Begin Quote :-
Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Those 'Gaps' can only be produced by 6 different combinations :-
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

In general, the number of combinations for any gap combinations would
be 49 - SUM(Gaps) - 5
For the example above, 49 - 38 - 5 = 6 combinations.
There will be lots of combinations of Gaps that can only be produced
by one combination.
End Quote.

Thanks again.
All the Best.
Paul

Paul,

Try the macro below

HTH,
Bernie
MS Excel MVP

Private Sub Gaps2()

Dim A As Integer
Dim B As Integer
Dim C As Integer
Dim D As Integer
Dim E As Integer
Dim F As Integer
Dim i As Integer
Dim GapsTotal(0 To 43) As Long

Application.ScreenUpdating = False

For i = 0 To 43
GapsTotal(i) = 0
Next i

For A = 1 To 44
For B = A + 1 To 45
For C = B + 1 To 46
For D = C + 1 To 47
For E = D + 1 To 48
For F = E + 1 To 49

GapsTotal(B - A - 1) = GapsTotal(B - A - 1) + 1
GapsTotal(C - B - 1) = GapsTotal(C - B - 1) + 1
GapsTotal(D - C - 1) = GapsTotal(D - C - 1) + 1
GapsTotal(E - D - 1) = GapsTotal(E - D - 1) + 1
GapsTotal(F - E - 1) = GapsTotal(F - E - 1) + 1

Next F
Next E
Next D
Next C
Next B
Next A

Sheets("Gaps Data").Range("B2").Value = "Gaps"
Sheets("Gaps Data").Range("C2").Value = "Total"

For i = 0 To 43
Sheets("Gaps Data").Cells(i + 3, 2).Value = "Gaps of " & Format(i, "00")
Sheets("Gaps Data").Cells(i + 3, 3).Value = GapsTotal(i)
Next i

Application.ScreenUpdating = True
End Sub


"Paul Black" wrote in message
oups.com...
Thanks for the reply Bernie,

The Gaps 06 06 08 12 06 = x combinations ( x could be 925,365
combinations with the exact same Gaps between the balls 1 & 2, and 2 &
3, and 3 & 4, and 4 & 5, and 5 & 6 ) is only an example figure, I have
no idea what the actual figure is, or come to it, how to code it.

There can only be 5 criteria for each combination. These are the gaps
between balls ...
1 and 2
2 and 3
3 and 4
4 and 5
5 and 6
... obviously with ALL 13,983,816 combinations there will be quite a
few categories.
The Gaps are produced for each category using all the 6 numbers within
each combination.

Begin Quote :-
Gaps 01 01 01 01 01 39 ( how did you get the 6 sets of
numbers? ) ...
... would be uniquely 01 03 05 07 09 49
End Quote.

I don't quite understand it when you say ...

Begin Quote :-
Gaps 06 06 08 12 06 = x combinations ( x could be 925,365 combinations
with the exact same Gaps between the balls 1-2, 2-3 ,3-4 ,4-5 & 5-6 )

Those 'Gaps' can only be produced by 6 different combinations :-
01 08 15 24 37 44
02 09 16 25 38 45
03 10 17 26 39 46
04 11 18 27 40 47
05 12 19 28 41 48
06 13 20 29 42 49

In general, the number of combinations for any gap combinations would
be 49 - SUM(Gaps) - 5
For the example above, 49 - 38 - 5 = 6 combinations.
There will be lots of combinations of Gaps that can only be produced
by one combination.
End Quote.

Thanks again.
All the Best.
Paul