How many different combinations of 5 numbers = 28

[Michaelsrk]

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

I'm asking for help because if I forget any possible pattern it will ruin my experiment.

 

[Deleted member 4993]

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

I'm asking for help because if I forget any possible pattern it will ruin my experiment.

If I were to conduct this project I would set up an excel sheet and make an exhaustive list:

99811
99181
99118
91981

and so on....

please share what you get - then we can fill in any gap.....

 

[Harry_the_cat]

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

I'm asking for help because if I forget any possible pattern it will ruin my experiment.

Are we to assume that all numbers must be integers/ positive / can't be 0 ??

 

[Michaelsrk]

Are we to assume that all numbers must be integers/ positive / can't be 0 ??

yes.

I forgot to mention we only need thew combination with 5 numbers.

 

[Deleted member 4993]

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

I'm asking for help because if I forget any possible pattern it will ruin my experiment.

one way to look at it be to ask:

How many 5 digit numbers can you make out of 99811? +

How many 5 digit numbers can you make out of 99721? +

How many 5 digit numbers can you make out of 99622? +

How many 5 digit numbers can you make out of 99631? +

How many 5 digit numbers can you make out of 99541? +

How many 5 digit numbers can you make out of 99532?

and so on..... (corrected 5 digit numbers)

 

[Michaelsrk]

one way to look at it be to ask:

How many 5 digit numbers can you make out of 99811? +

How many 5 digit numbers can you make out of 99721? +

How many 5 digit numbers can you make out of 99622? +

How many 5 digit numbers can you make out of 99631? +

How many 5 digit numbers can you make out of 99541? +

How many 5 digit numbers can you make out of 99532?

and so on.....

I don't understand but that seems way more complicated then I am asking.
I just need five 1 digit numbers that add together to equal 28, but I need all off them.

 

[pka]

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

I assume that five-digit numbers you mean the first digit must be at least one. Thus 10999 would be counted.
Now look at this expansion. In that expansion the term \(\displaystyle 4170x^{28}\) tells us that there are four thousand one hundred and seventy five digits numbers that have a digit-sum of twenty-eight.

If I have misunderstood the set-up please correct me.

 

[Michaelsrk]

I assume that five-digit numbers you mean the first digit must be at least one. Thus 10999 would be counted.
Now look at this expansion. In that expansion the term \(\displaystyle 4170x^{28}\) tells us that there are four thousand one hundred and seventy five digits numbers that have a digit-sum of twenty-eight.

If I have misunderstood the set-up please correct me.

I don't mean 5 digits I mean 5 numbers total.

 

[pka]

I don't mean 5 digits I mean 5 numbers total.

What is the possible difference?
What is the difference in 10999 & 1+0+9+9+9=28?
How is there any difference in looking at the digit-sum of a five digit number and the sum of five digits?
By the way, this is a very well known class of problems.

 

[Michaelsrk]

What is the possible difference?
What is the difference in 10999 & 1+0+9+9+9=28?
How is there any difference in looking at the digit-sum of a five digit number and the sum of five digits?
By the way, this is a very well known class of problems.

I have no idea, I am just asking how many combinations of five numbers being equal to 28 is there. (without zero)

 

[pka]

I have no idea, I am just asking how many combinations of five numbers being equal to 28 is there. (without zero)

You said nothing about not using zero.
In each example you gave you used only digits.
You now appear to be asking a different sort of question.
10+1+11+2+1+3=28 is a example of five numbers adding to 28. Is that an example of what you mean?
If it is, do you count 1+1+2+3+10+11=28 as different from above?

If your answer is no they are the same, then you are into a totally different counting question.
This is an area known as integer partitions. In this case the question is how many ways can 28 be partitioned into exactly five non-trivial summands. The answer turns out very difficult to calculate using recursive functions.

Look at your original post.

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

Those are not at all examples which illustrate exactly what your questions means. If you do not ask a very clearly understandable question, you have no reason to expect us to read your mind.

 

[Michaelsrk]

You said nothing about not using zero.
In each example you gave you used only digits.
You now appear to be asking a different sort of question.
10+1+11+2+1+3=28 is a example of five numbers adding to 28. Is that an example of what you mean?
If it is, do you count 1+1+2+3+10+11=28 as different from above?

If your answer is no they are the same, then you are into a totally different counting question.
This is an area known as integer partitions. In this case the question is how many ways can 28 be partitioned into exactly five non-trivial summands. The answer turns out very difficult to calculate using recursive functions.

Look at your original post.

Those are not at all examples which illustrate exactly what your questions means. If you do not ask a very clearly understandable question, you have no reason to expect us to read your mind.

How many one digit numbers = 28 using 5 one digit numbers each time.no numbers with zero, simply 1-9.

sorry for being unclear it makes perfect sense to me.

 

[pka]

There are 3510 of the critters! Correct
In ascending order:
1: 11899
2: 11989
...
3509: 99721
3510: 99811

See this expansion. That can be used for any sum 5 to 45.

The term \(\displaystyle 2030x^{32}\) tells us that there are 2030 such numbers which sum to 32.

 

[Michaelsrk]

I really don't understand. You are saying there are 3501 combinations that equal 28 only using the digits 1-9?

9+9+7+2+1=28
9+9+6+2+2=28
9+9+5+3+2=28
9+9+4+4+2=28

So if I where to write them all out there would be 3501?

 

[ksdhart2]

I really don't understand. You are saying there are 3501 combinations that equal 28 only using the digits 1-9?

9+9+7+2+1=28
9+9+6+2+2=28
9+9+5+3+2=28
9+9+4+4+2=28

So if I where to write them all out there would be 3501?

Well, not quite. There would be 3510.

 

[Michaelsrk]

Well, not quite. There would be 3510.

Well I did have a theory on how to increase your odds at winning the lottery using a base 9 system but if that is correct there is no way I could do it without using a million+ numbers

 

[Michaelsrk]

Well I did have a theory on how to increase your odds at winning the lottery using a base 9 system but if that is correct there is no way I could do it without using a million+ numbers

Here are the first couple patterns I created using just the one possible set.

1.Wed, Jan 11, 2017

7 17 23 32 39
7+8+5+5+3=(28)
9=9 18,27,36
8=8,17,26,35
7=7,16,25,34
6=6,15,24,33
5=5,14,23,32
4=4,13,22,31
3=3,12,21,30
2=2,2,11,20,29
1=1,10,19,28

9+9+7+2+1



9+9+6+2+2

9,27,6,2,20
9,27,15,2,20
9,27,24,2,20
9,27,33,2,20

9,27,6,2,11
9,27,15,2,11
9,27,24,2,11
9,27,33,2,11

9,36,6,2,20
9,36,15,2,20
9,36,24,2,20
9,36,33,2,20

18,36,6,11,2
18,36,24,11,2
18,36,33,11,2
18,36,15,11,2

18,27,6,2,20
18,27,15,2,20
18,27,24,2,20
18,27,33,2,20

18,27,6,11,20
18,27,15,11,20
18,27,24,11,20
18,27,33,11,20

18,27,33,11,29
18,27,24,11,29
18,27,15,11,29
18,27,6,11,29

18,27,33,2,29
18,27,24,2,29
18,27,15,2,29
18,27,6,2,29


18,36,6,11,2
18,36,24,11,2
18,36,33,11,2
18,36,15,11,2


18,36,6,2,20
18,36,15,2,20
18,36,24,2,20
18,36,33,2,20

18,36,6,11,29
18,36,15,11,29
18,36,24,11,29
18,36,33,11,29

 

[Otis]

10+1+11+2+1+3=28 is [an] example of five numbers adding to 28.

Oops, that's an example of six numbers whose sum is 28.

 

[Harry_the_cat]

I need the numbers to all add together to equal 28 and I need all the possible ways to do it, such as.
9+9+7+2+1
9+9+6+2+2

I'm asking for help because if I forget any possible pattern it will ruin my experiment.

Are 9+9+7+2+1 and 9+9+7+1+2 and 1+2+9+7+9 counted as three different ways? Or are they to be considered the same(ie they use the same numbers)?

 

[pka]

Michael, why don't you start over and post
a CLEAR question...along with an example.

Ahem!