combination of integer numbers

I need to make distibution of 15 apples among 4 person [a b c d],

each person can have a value betwwen 0-15. and summation always (a+b+c+d=15)

so how can i generate the matrix for all possible combinantion

so i eapect matrix as

a = [1 14 0 0

0 0 0 15

3 6 2 4

...................

...................]

[Walter Roberson]

One approach is to ndgrid() all possible combinations, and then check those to find the ones that add up to the right number.

[Nasser Hakami]

thanks. however i couldn't manage to do it

Answer 1

[the cyclist]

I would download John D'Errico's partitions function, and then I believe your answer is

p = partitions(15,[1 1 1 1])

[Nasser Hakami]

tahnks. It look great code. but i coulnt mange to run correctly. i will try again to adapt it

[the cyclist]

Do you mean that the code will not work for you, or that you do not get the result you expect?

(FYI, Walter's solution and this one give the same result.)

[Nasser Hakami]

first tahnks for your feedback

to answer you: i could not mange to run the code

i will try to make exampele easier

4 apples, 2 person. so ALL combinations are

[0    4
1    3
2    2
3    1
4    0]

if 4 apples , 3 persons. combination are

[0    0    4
0    1    3
0    2    2
0    3    1
0    4    0
1    0    3
1    1    2
1    2    1
1    3    0
2    0    2
2    1    1
2    2    0
3    0    1
3    1    0
4    0    0]

[the cyclist]

I don't think an easier example was needed, but I can verify that

partitions(4,[1 1 1])

gives the same answer (not necessarily in the same row order).

I'm not sure why you couldn't run the code. Did you do the following?

• go to the link I uploaded
• click on the download button to get the files
• unzip the files
• put the partitions.m file in your path so that you can run it

[Nasser Hakami]

thanks a lot

it is working perfect

the problem that i just copied the code from webpage and i didnt download file

Answer 2

[Walter Roberson]

[Ag, Bg, Cg, Dg] = ndgrid(0:15);
Eg = [Ag(:), Bg(:), Cg(:), Dg(:)];
mask = sum(Eg,2) == 15;
selected = Eg(mask,:);
a = selected(:,1);
b = selected(:,2);
c = selected(:,3);
d = selected(:,4);