Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

If it was just one player against another, you can set this up in a
simple table like this:

P B R O G
Purple (P) x y y y y
Blue (B) y x y y y
Red (R) y y x y y
Orange (O) y y y x y
Green (G) y y y y x

the x's in the table indicate that P cannot play P etc. The table
covers home and away type fixtures, with the home side in column A and
the away side in row 1. If this is a golfing competition, for example,
where this does not apply, then you can remove the triangle of matches
above the leading diagonal of x's, so tht you have something like this:

P B R O G
Purple (P) x
Blue (B) y x
Red (R) y y x
Orange (O) y y y x
Green (G) y y y y x

You can apply the same principle with pairs - you just need to write
down all possible combinations. Assuming P & B is the same as B & P,
you would have this down column A:

PB
PR
PO
PG
BR
BO
BG
RO
RG
OG

Repeat the list going across, ignore the diagonal, and count the y's.

Is this what you wanted? You can do this on a piece of paper or type it
all into Excel and then print it out onto a piece of paper!

Hope this helps.

Pete


Steven Sinclair wrote:
Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

Steven,

It depends whether you need to distniguish between the order of the players
or not. The mathematical functions Permutation and Combine will caculate the
number of ways in which any number of items can be put together in sets
comprising a certain number of items, with Perm finding the number of ordered
sets and Combine the total number of sets irrespective of order. They use
the mathematical function "factorial" which is the product of a whole number
(integer) and all the numbers less than it down to 1. So factorial 3 is
3x2x1=6, factorial 4 is 4x3x2x1=24, etc. Combine will divide the factorial
of the number of items by the factorial of the number of sets. So 3 items
combined in sets of 2 will give 3, and Perm will give 6, etc. These
functions are available in Excel under the names PERMUT and COMBIN

"Steven Sinclair" wrote:

Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

Okay.

So if I use the PERMUT function, I get 20. If I use the COMBIN function, I
get 10. Does that mean my answer would be 30?

Thanx again.

"Bill W" wrote:

Steven,

It depends whether you need to distniguish between the order of the players
or not. The mathematical functions Permutation and Combine will caculate the
number of ways in which any number of items can be put together in sets
comprising a certain number of items, with Perm finding the number of ordered
sets and Combine the total number of sets irrespective of order. They use
the mathematical function "factorial" which is the product of a whole number
(integer) and all the numbers less than it down to 1. So factorial 3 is
3x2x1=6, factorial 4 is 4x3x2x1=24, etc. Combine will divide the factorial
of the number of items by the factorial of the number of sets. So 3 items
combined in sets of 2 will give 3, and Perm will give 6, etc. These
functions are available in Excel under the names PERMUT and COMBIN

"Steven Sinclair" wrote:

Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

Okay...

According to Pete's method, I come up with 15 unique games possible.

However, utilizing Bill's method, I get 20 for the permutations and 10 for
the combinations.

Is there a formula or function that will actually figure this correctly?

Thanx.

"Pete_UK" wrote:

If it was just one player against another, you can set this up in a
simple table like this:

P B R O G
Purple (P) x y y y y
Blue (B) y x y y y
Red (R) y y x y y
Orange (O) y y y x y
Green (G) y y y y x

the x's in the table indicate that P cannot play P etc. The table
covers home and away type fixtures, with the home side in column A and
the away side in row 1. If this is a golfing competition, for example,
where this does not apply, then you can remove the triangle of matches
above the leading diagonal of x's, so tht you have something like this:

P B R O G
Purple (P) x
Blue (B) y x
Red (R) y y x
Orange (O) y y y x
Green (G) y y y y x

You can apply the same principle with pairs - you just need to write
down all possible combinations. Assuming P & B is the same as B & P,
you would have this down column A:

PB
PR
PO
PG
BR
BO
BG
RO
RG
OG

Repeat the list going across, ignore the diagonal, and count the y's.

Is this what you wanted? You can do this on a piece of paper or type it
all into Excel and then print it out onto a piece of paper!

Hope this helps.

Pete


Steven Sinclair wrote:
Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

Take a look at the Help items for each of these functions - they probably
explain the theory better than I can. Whether to use PERMUT or COMBIN
depends on whether you need to distinguish between the partnership of (say)
Purple and Blue and the partnership of Blue and Purple, and this may well
depend upon the game they are playing.

Re-reading your question I realise that you need to calculate the number of
games that can be played by any two two-person partnerships from five
players. This you can do manually and it is 15. You select two players (say
Purple and Blue and work out how many more partnerships can be made with the
remaining three players, which is three. You will get duplication by doing
it manually and then need to delete the duplicates.

Mathematically you are selecting any two players from five, and matching
them with any two from the remaining three. If the order of the sets of two
players is unimportant you use COMBIN. And the number of games is calculated
using COMBIN(5,2) multiplied by COMBIN(3,2), because when the first two
players have been paired, there are three remaining from which two are
selected. This is 15, which is correct. If you are concerned about the order
of the set of two players, then use PERMIT in both formulae, which gives 120.
I'll let you check that manually!

"Steven Sinclair" wrote:

Okay.

So if I use the PERMUT function, I get 20. If I use the COMBIN function, I
get 10. Does that mean my answer would be 30?

Thanx again.

"Bill W" wrote:

Steven,

It depends whether you need to distniguish between the order of the players
or not. The mathematical functions Permutation and Combine will caculate the
number of ways in which any number of items can be put together in sets
comprising a certain number of items, with Perm finding the number of ordered
sets and Combine the total number of sets irrespective of order. They use
the mathematical function "factorial" which is the product of a whole number
(integer) and all the numbers less than it down to 1. So factorial 3 is
3x2x1=6, factorial 4 is 4x3x2x1=24, etc. Combine will divide the factorial
of the number of items by the factorial of the number of sets. So 3 items
combined in sets of 2 will give 3, and Perm will give 6, etc. These
functions are available in Excel under the names PERMUT and COMBIN

"Steven Sinclair" wrote:

Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

Interesting...

If I use the formula you suggest "...combin(5,2) multiplied by
combin(3,2)..." I end up with a value of 30. So, how do we end up with 15?
Are we simply taking our total of 30 and dividing that by two due to the fact
that we're pairing up the people?

Thanx again.

"Bill W" wrote:

Take a look at the Help items for each of these functions - they probably
explain the theory better than I can. Whether to use PERMUT or COMBIN
depends on whether you need to distinguish between the partnership of (say)
Purple and Blue and the partnership of Blue and Purple, and this may well
depend upon the game they are playing.

Re-reading your question I realise that you need to calculate the number of
games that can be played by any two two-person partnerships from five
players. This you can do manually and it is 15. You select two players (say
Purple and Blue and work out how many more partnerships can be made with the
remaining three players, which is three. You will get duplication by doing
it manually and then need to delete the duplicates.

Mathematically you are selecting any two players from five, and matching
them with any two from the remaining three. If the order of the sets of two
players is unimportant you use COMBIN. And the number of games is calculated
using COMBIN(5,2) multiplied by COMBIN(3,2), because when the first two
players have been paired, there are three remaining from which two are
selected. This is 15, which is correct. If you are concerned about the order
of the set of two players, then use PERMIT in both formulae, which gives 120.
I'll let you check that manually!

"Steven Sinclair" wrote:

Okay.

So if I use the PERMUT function, I get 20. If I use the COMBIN function, I
get 10. Does that mean my answer would be 30?

Thanx again.

"Bill W" wrote:

Steven,

It depends whether you need to distniguish between the order of the players
or not. The mathematical functions Permutation and Combine will caculate the
number of ways in which any number of items can be put together in sets
comprising a certain number of items, with Perm finding the number of ordered
sets and Combine the total number of sets irrespective of order. They use
the mathematical function "factorial" which is the product of a whole number
(integer) and all the numbers less than it down to 1. So factorial 3 is
3x2x1=6, factorial 4 is 4x3x2x1=24, etc. Combine will divide the factorial
of the number of items by the factorial of the number of sets. So 3 items
combined in sets of 2 will give 3, and Perm will give 6, etc. These
functions are available in Excel under the names PERMUT and COMBIN

"Steven Sinclair" wrote:

Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.

Sorry forgot to mention that you wil get duplicates in the formula
calculation as in the manual one. When you select say Purple and Blue and
let them play Orange and Green this is the same as Orange and Green playing
Purple and Blue. Try it manually by writing down the different combinations.
So the formula should contain a divide by 2 element, i.e.
COMBIN(5,2)*COMBIN(3,2)/2.

"Steven Sinclair" wrote:

Interesting...

If I use the formula you suggest "...combin(5,2) multiplied by
combin(3,2)..." I end up with a value of 30. So, how do we end up with 15?
Are we simply taking our total of 30 and dividing that by two due to the fact
that we're pairing up the people?

Thanx again.

"Bill W" wrote:

Take a look at the Help items for each of these functions - they probably
explain the theory better than I can. Whether to use PERMUT or COMBIN
depends on whether you need to distinguish between the partnership of (say)
Purple and Blue and the partnership of Blue and Purple, and this may well
depend upon the game they are playing.

Re-reading your question I realise that you need to calculate the number of
games that can be played by any two two-person partnerships from five
players. This you can do manually and it is 15. You select two players (say
Purple and Blue and work out how many more partnerships can be made with the
remaining three players, which is three. You will get duplication by doing
it manually and then need to delete the duplicates.

Mathematically you are selecting any two players from five, and matching
them with any two from the remaining three. If the order of the sets of two
players is unimportant you use COMBIN. And the number of games is calculated
using COMBIN(5,2) multiplied by COMBIN(3,2), because when the first two
players have been paired, there are three remaining from which two are
selected. This is 15, which is correct. If you are concerned about the order
of the set of two players, then use PERMIT in both formulae, which gives 120.
I'll let you check that manually!

"Steven Sinclair" wrote:

Okay.

So if I use the PERMUT function, I get 20. If I use the COMBIN function, I
get 10. Does that mean my answer would be 30?

Thanx again.

"Bill W" wrote:

Steven,

It depends whether you need to distniguish between the order of the players
or not. The mathematical functions Permutation and Combine will caculate the
number of ways in which any number of items can be put together in sets
comprising a certain number of items, with Perm finding the number of ordered
sets and Combine the total number of sets irrespective of order. They use
the mathematical function "factorial" which is the product of a whole number
(integer) and all the numbers less than it down to 1. So factorial 3 is
3x2x1=6, factorial 4 is 4x3x2x1=24, etc. Combine will divide the factorial
of the number of items by the factorial of the number of sets. So 3 items
combined in sets of 2 will give 3, and Perm will give 6, etc. These
functions are available in Excel under the names PERMUT and COMBIN

"Steven Sinclair" wrote:

Here's what I have...

Purple
Blue
Red
Orange
Green

Each of the colors represent a player.
Each of the players needs a partner.
Each set of partners needs to play with another set of partners.
Each player needs to play with a different partner against all other partners.

All-in-all, we need to count how many games can be played with how many
UNIQUE partners and UNIQUE opposing partners.

I have no idea of even where to begin other than just writing everything out
by hand on a piece of paper.

Thanx.