How to solve following task?

Hello,

I have a problem and can't think of the solution.

Lets say:

I have an paper roll with the width of 60cm. I need to cut the rool in to 3 parts of: 28, 20 and 15cm + left over (if any)

I need to find all the variations of the cuts and the left overs. (from the image (x1,x2,x3,x4,xn..))

I think that I would need to make an equation 28A+20B+15C+D=60 , while D<15 . D=[0:1:14]

But only integers should be used.

Any help would be appreciated.

Thank you.

[Torsten]

I wonder why your paper roll has a width of 65. All your combinations in the table lead to a roll width of 60:

60 = 2*28 + 4 = 28+20+12 = ...

[Vejas]

Sorry for that, it was a typo. Will fix it right now

Answer 1

[Dyuman Joshi]

The values you have add up to 60 and not 65.

Total=60;
a=28;
b=20;
c=15;

[A,B,C]=meshgrid(0:floor(Total/a), 0:floor(Total/b), 0:floor(Total/c));
arr = Total-(a*A+b*B+c*C);
%Indices of values which satisfy the condition on D
k = arr>=0 & arr<15;

%Obtain the final output using the indices
out = [A(k) B(k) C(k) abs(arr(k))]'

out = 4×7

0 1 2 0 0 1 0 3 1 0 2 1 0 0 0 0 0 1 2 2 4 0 12 4 5 10 2 0

[Vejas]

Thank you so much, works perfectly