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Calculate the Number of Subsets

Author
5 Mar 2006 3:47 PM
Paul Black
Hi Everyone,

This is Lotto Based.
There is a System in Lotto called "Wheels".
A Lotto Wheeling System is a Special Pattern to Arrange Numbers into
Combinations. This System can be Used Over and Over again with
Different
Numbers. A Lotto Wheel is Constructed in such a way that if the Winning

Numbers Fall in the Group of Numbers you have Selected, you will Always

have a Winning Combination Somewhere. If for Example, you have a Group
of 12 Numbers then the Lotto Wheel you Select should have the Numbers
1-12 Arranged in Sets of Numbers ( Each Set is 6 Numbers ). You then
take the Wheel and Substitute your Numbers in the Wheels Pattern and
Simply Replace all the 1's in the Pattern with your First Number, all
the 2's with your Second Number, all the 3's with your Third Number,
etc. All Wheels give a Guarantee. For Example, the Wheel 24,6,3,6,50
Means, there are 24 Different Numbers Used in the Wheel, there are 6
Numbers Drawn, the Guarantee of having 3 Numbers in at Least 1
Combination if ALL the 6 Numbers Drawn are in the Selected 24 Numbers.
I have a Set of 6 Number Combinations in Cells "G13:L27" ( the Number
of
Combinations could be More or Less ).
In this Example I am Using a Wheel with 24 Numbers :-

1,3,7,12,15,16
1,4,5,17,20,21
1,8,9,10,19,22
1,13,14,18,23,24
2,3,6,9,21,23
2,10,12,14,16,20
2,11,15,19,20,24
3,4,7,10,18,24
3,5,7,14,17,19
4,6,8,14,15,22
4,9,11,13,16,19
5,10,13,15,17,23
5,11,12,18,21,22
6,8,12,16,17,24
7,8,13,20,22,23

Here is the Code that someone has Kindly Provided which Cycles through
ALL Combinations and Compares ALL the Combinations with ALL the
Combinations in the Above Wheel. The Below Code Finds the Coverage (
Total Combinations ) of 5 Numbers if 5 Numbers are Matched ...

Code:
Sub test_5()
Dim a, dic As Object
Set dic = CreateObject("Scripting.Dictionary")
a = Range("g13").CurrentRegion.Value
For i = 1 To UBound(a, 1)
    For ii = 1 To 2
        For iii = ii + 1 To 3
            For iv = iii + 1 To 4
                For v = iv + 1 To 5
                    For vi = v + 1 To 6
                        z = a(i, ii) & "," & a(i, iii) & a(i, iv) &
a(i,
v) & a(i, vi)
                        If Not dic.exists(z) Then
                            dic.Add z, Nothing
                            n = n + 1
                        End If
Next vi, v, iv, iii, ii, i
Set dic = Nothing
Range("O16") = n
End Sub

.... and Produces the Correct Result of 90.
How can the Code be Modified to Also Produce the Combinations Covered
for the Categories ...

Matched = Covered Combinations
2 if 5 = 42,504
3 if 5 = 35,720
4 if 5 = 4,140
5 if 5 = 90 ( the Code Already Provides this Result )

.... Please.
I was Told for the Interpretation of the 3 if 5 Category that you Need
to Cycle through ALL 5 Number Combinations that can be Constructed from

the Total Numbers Used in the Wheel ( 24 in this Case ). So if the
Wheel
Contains "x" Unique Numbers, you Need to Cycle through ALL 5 Number
Combinations from those "x" Numbers. Then you Need to Scan the Wheel
for
Each 5 Number Combination Produced and Compare it with Each Line in the

Wheel to see if that Line Matches the 5 Number Combination in *EXACTLY*

3 Numbers. If it does, then that Combination of 3 if 5 is Covered and
Added to the Total and there is NO Need to Continue to Check for that
Particular Combination Any Further. You then go onto the Next
Combination to Check and so on Until ALL Combinations have been Cycled
through and Checked with the Wheel.

I Hope I have Explained this Clear Enough.
Many Thanks in Advance.
All the Best.
Paul

Author
5 Mar 2006 11:44 PM
Michael C
Show quote Hide quote
"Paul Black" <paul_blac***@hotmail.com> wrote in message
news:1141573676.458315.313910@i39g2000cwa.googlegroups.com...
> Hi Everyone,
>
> This is Lotto Based.
> There is a System in Lotto called "Wheels".
> A Lotto Wheeling System is a Special Pattern to Arrange Numbers into
> Combinations. This System can be Used Over and Over again with
> Different
> Numbers. A Lotto Wheel is Constructed in such a way that if the Winning
......
> 3 Numbers. If it does, then that Combination of 3 if 5 is Covered and
> Added to the Total and there is NO Need to Continue to Check for that
> Particular Combination Any Further. You then go onto the Next
> Combination to Check and so on Until ALL Combinations have been Cycled
> through and Checked with the Wheel.


woooooooo, way too much text. Can you shorten your question, most won't read
all the way through that? :-)

Michael
Author
6 Mar 2006 6:14 PM
Alfie [UK]
On Mon, 6 Mar 2006 10:44:13 +1100, "Michael C" <nospam@nospam.com>
wrote:
>woooooooo, way too much text. Can you shorten your question, most won't read
>all the way through that? :-)
>
Unles you're being ironic, Paul posted his original shorter question in
Message-ID: <1140348667.729220.156***@o13g2000cwo.googlegroups.com>
'Subject: If ... Then Loop ?' on 19th Feb and was asked to clarify some
of the terminology and define more clearly what help he was after, hence
I presume this longer post :)
--
Alfie
<http://www.delphia.co.uk/>
When you do not fear death, it's spectre no longer holds power over you. Without such weight upon your shoulders, you become free to live at last.
Author
6 Mar 2006 9:47 PM
Michael C
"Alfie [UK]" <m*@privacy.net> wrote in message
news:rquo021q7pk2ai7hjf5rookgf8ckkc6jea@4ax.com...
> On Mon, 6 Mar 2006 10:44:13 +1100, "Michael C" <nospam@nospam.com>
> wrote:
>>woooooooo, way too much text. Can you shorten your question, most won't
>>read
>>all the way through that? :-)
>>
> Unles you're being ironic, Paul posted his original shorter question in
> Message-ID: <1140348667.729220.156***@o13g2000cwo.googlegroups.com>
> 'Subject: If ... Then Loop ?' on 19th Feb and was asked to clarify some
> of the terminology and define more clearly what help he was after, hence
> I presume this longer post :)

I'd suggest he has failed to meet a happy medium :-) So far no answers.....

Michael
Author
6 Mar 2006 6:57 PM
Jeff Johnson [MVP: VB]
Show quote Hide quote
"Michael C" <nospam@nospam.com> wrote in message
news:u2sRc4KQGHA.3856@TK2MSFTNGP12.phx.gbl...

>> Hi Everyone,
>>
>> This is Lotto Based.
>> There is a System in Lotto called "Wheels".
>> A Lotto Wheeling System is a Special Pattern to Arrange Numbers into
>> Combinations. This System can be Used Over and Over again with
>> Different
>> Numbers. A Lotto Wheel is Constructed in such a way that if the Winning
> .....
>> 3 Numbers. If it does, then that Combination of 3 if 5 is Covered and
>> Added to the Total and there is NO Need to Continue to Check for that
>> Particular Combination Any Further. You then go onto the Next
>> Combination to Check and so on Until ALL Combinations have been Cycled
>> through and Checked with the Wheel.
>
>
> woooooooo, way too much text.

For me, it's Way Too Many Extraneous Capital Letters. Unless this is the
longest book title ever....
Author
8 Mar 2006 7:49 PM
Bob O`Bob
Jeff Johnson [MVP: VB] wrote:
Show quoteHide quote
> "Michael C" <nospam@nospam.com> wrote in message
> news:u2sRc4KQGHA.3856@TK2MSFTNGP12.phx.gbl...
>
>>> Hi Everyone,
>>>
>>> This is Lotto Based.
>>> There is a System in Lotto called "Wheels".
>>> A Lotto Wheeling System is a Special Pattern to Arrange Numbers into
>>> Combinations. This System can be Used Over and Over again with
>>> Different
>>> Numbers. A Lotto Wheel is Constructed in such a way that if the Winning
>> .....
>>> 3 Numbers. If it does, then that Combination of 3 if 5 is Covered and
>>> Added to the Total and there is NO Need to Continue to Check for that
>>> Particular Combination Any Further. You then go onto the Next
>>> Combination to Check and so on Until ALL Combinations have been Cycled
>>> through and Checked with the Wheel.
>>
>> woooooooo, way too much text.
>
> For me, it's Way Too Many Extraneous Capital Letters. Unless this is the
> longest book title ever....
>
>

not to mention too many separate message threads.



    Bob
--
okay, fine, so I just did.  deal.
Author
11 Mar 2006 9:02 AM
Paul Black
Thanks to everyone who has replied.
I have been off line for a while so appologies for not answering
sooner.
I think I have probably used the word subset in error. I am basically
just trying to cycle through the combinations already in the Wheel and
find out the coverage ( total combinations for each category ).

Any other help will be appreciated.
Thanks in advance.
All the Best.
Paul