Hi everyone,

I would like an algorithm or code to work out how many subset
combinations with specific criteria are covered when compared with
combinations in a wheel. A wheels criteria is as follows :-

Description = C(n,k,t,m)=b where :-

n=the number of balls drawn from (i.e. 49).
k=the number of balls drawn (i.e. 6).
t=the total balls to match to guarantee a win.
m=the criteria that has to be met in order to guarantee t win, m
defines the least number of balls from our n set that must be correct.
b=the total combinations in the wheel.

The formula to calculate the total combinations is :-
.........................n!
C(n, k) = -------------------
....................k! (n - k) !


The formula to calculate the subsets (the coefficient) is ...
.........................n!
C(n, m) = -------------------
....................m! (n - m) !

.... where n! is n factorial and is equal to n*(n-1)*(n-2)* ... *2*1.

The above was taken from :-
http://mathforum.org/library/drmath/view/60881.html

I manually input combinations of 6 numbers into a spreadsheet named
"Data" in cells "B3:G?".
We will use the 2 if 5, 3 if 5, 4 if 5 and 5 if 5 categories to
explain what I am trying to achieve.
For the 2 if 5 category, this requires calculating ALL the 5 number
combinations available from "n" which would be C(n, k) where "n" is 49
(or the maximum number used in the wheel) and "k" is 5.
The category 2 if 5 means, that "IF" at "LEAST" 2 numbers in ANY of
the 5 number combinations matches 2 numbers in ANY of the 6 number
combinations in the wheel, then those 5 number combinations have
satisfied the 2 if 5 scenario and are therefore covered. You then add
1 to the 2 if 5 category total for each of the 5 number combinations
that has satisfied the 2 if 5 scenario.
For the 2 if 5 scenario, there is NO need to list the C(n,5)
combinations because I ONLY want the total combinations covered for
the 2 if 5 category, not the actual combinations themselves. Anyway,
the 5 number combinations ONLY need to be calculated for the highest
"n" number in the wheel, this could be 12 [ C(12,5) ], 15 [ C15,5) ],
20 [ C(20,5) ], 30 [ (30,5) ] etc.
Basically, the program needs to iterate through ALL the 5 number
combinations from "n" and check each one to see if there is at "LEAST"
2 numbers in ANY of the 6 number combinations in the spreadsheet. If
there is, 1 is added to the category covered total for each 5 number
combination that satisfies the 2 if 5 scenario.
The same principle and structure applies for the 3 if 5, 4 if 5 and 5
if 5 categories.

If we use the 5 number combinations as "x" for example, and the 6
number combinations as "y" for example, this is roughly what should
happen :-

If x matches y in = 2 numbers Then
Category 2 if 5 Total = + 1
If x matches y in = 3 numbers Then
Category 3 if 5 Total = + 1
If x matches y in = 4 numbers Then
Category 4 if 5 Total = + 1
If x matches y in EXACTLY 5 numbers Then
Category 5 if 5 Total = + 1
End If
End If
End If
End If

Thanks in Advance.
All the Best.
Paul

Hi,

Maybe the code to produce the 5 number combinations would look
something like this :-

Option Explicit
Option Base 1

Sub Produce_5_Number_Combinations()

Dim A as Integer
Dim B as Integer
Dim C as Integer
Dim D as Integer
Dim E as Integer
Dim MinVal As Integer
Dim MaxVal As Integer

Application.ScreenUpdating = False

MinVal = 1
MaxVal = Whatever the highest number is in the sheet named "Data" and
in the Range "B3:G?".

For A = 1 to MaxVal - 4
For B = A + 1 to MaxVal - 3
For C = B + 1 to MaxVal - 2
For D = C + 1 to MaxVal - 1
For E = D + 1 to MaxVal

*** Code for the ? if 5 scenario goes here maybe ***

Next E
Next D
Next C
Next B
Next A

*** The 2 if 5 category total will go in the sheet named "Statistics"
and in Cell "D12" ***

Application.ScreenUpdating = True
End Sub

Thanks in Advance.
All the Best.
Paul

On Jul 26, 3:50 pm, Paul Black wrote:
Hi everyone,

I would like an algorithm or code to work out how many subset
combinations with specific criteria are covered when compared with
combinations in a wheel. A wheels criteria is as follows :-

Description = C(n,k,t,m)=b where :-

n=the number of balls drawn from (i.e. 49).
k=the number of balls drawn (i.e. 6).
t=the total balls to match to guarantee a win.
m=the criteria that has to be met in order to guarantee t win, m
defines the least number of balls from our n set that must be correct.
b=the total combinations in the wheel.

The formula to calculate the total combinations is :-
........................n!
C(n, k) = -------------------
...................k! (n - k) !

The formula to calculate the subsets (the coefficient) is ...
........................n!
C(n, m) = -------------------
...................m! (n - m) !

... where n! is n factorial and is equal to n*(n-1)*(n-2)* ... *2*1.

The above was taken from :-http://mathforum.org/library/drmath/view/60881.html

I manually input combinations of 6 numbers into a spreadsheet named
"Data" in cells "B3:G?".
We will use the 2 if 5, 3 if 5, 4 if 5 and 5 if 5 categories to
explain what I am trying to achieve.
For the 2 if 5 category, this requires calculating ALL the 5 number
combinations available from "n" which would be C(n, k) where "n" is 49
(or the maximum number used in the wheel) and "k" is 5.
The category 2 if 5 means, that "IF" at "LEAST" 2 numbers in ANY of
the 5 number combinations matches 2 numbers in ANY of the 6 number
combinations in the wheel, then those 5 number combinations have
satisfied the 2 if 5 scenario and are therefore covered. You then add
1 to the 2 if 5 category total for each of the 5 number combinations
that has satisfied the 2 if 5 scenario.
For the 2 if 5 scenario, there is NO need to list the C(n,5)
combinations because I ONLY want the total combinations covered for
the 2 if 5 category, not the actual combinations themselves. Anyway,
the 5 number combinations ONLY need to be calculated for the highest
"n" number in the wheel, this could be 12 [ C(12,5) ], 15 [ C15,5) ],
20 [ C(20,5) ], 30 [ (30,5) ] etc.
Basically, the program needs to iterate through ALL the 5 number
combinations from "n" and check each one to see if there is at "LEAST"
2 numbers in ANY of the 6 number combinations in the spreadsheet. If
there is, 1 is added to the category covered total for each 5 number
combination that satisfies the 2 if 5 scenario.
The same principle and structure applies for the 3 if 5, 4 if 5 and 5
if 5 categories.

If we use the 5 number combinations as "x" for example, and the 6
number combinations as "y" for example, this is roughly what should
happen :-

If x matches y in = 2 numbers Then
Category 2 if 5 Total = + 1
If x matches y in = 3 numbers Then
Category 3 if 5 Total = + 1
If x matches y in = 4 numbers Then
Category 4 if 5 Total = + 1
If x matches y in EXACTLY 5 numbers Then
Category 5 if 5 Total = + 1
End If
End If
End If
End If

Thanks in Advance.
All the Best.
Paul