permutations of 4 numbers in 7 positions IF the sum of the numbers is 600

I want to generate all permutations of 4 numbers in 7 places, but we have a condition that the sum of the 7 places should be 600.

my nambers are 100,125,75,50

It is clear that repetition is allowed.

How can i do that?

[Matt J]

It is clear that repetition is allowed.

If so, it is not a "permutation".

Answer 1

[the cyclist]

This is a "making change" problem, where the smaller numbers can represent coins, and the large number is the total of the change. You can use the makeChange function from the File Exchange to do this.

Below, I've generate all possible combinations. It wasn't clear to me if you need up to 7 numbers, or exactly 7 numbers, but you should be able to trim the list accordingly.

[count, combos] = makeChange(600,[125,100,75,50])

count = 41

combos = 41×4

4 1 0 0 4 0 0 2 3 1 1 1 3 0 3 0 3 0 1 3 2 2 2 0 2 2 0 3 2 1 2 2 2 1 0 5 2 0 4 1

Answer 2

[Matt J]

See the attached file.

combos = diophantine(ones(1,7),600,[0,100,125,75,50])

combos = 4585×7

125 125 125 125 100 0 0 125 125 125 100 125 0 0 125 125 100 125 125 0 0 125 100 125 125 125 0 0 100 125 125 125 125 0 0 125 125 125 125 0 100 0 100 100 100 100 100 100 0 75 125 100 100 100 100 0 125 75 100 100 100 100 0 75 100 125 100 100 100 0

all(sum(combos,2)==600)

ans = logical
   1

[Matt J]

Don't they?

combos = diophantine(ones(1,7),600,[0,100,125,75,50]);

all(sum(combos,2)==600)

ans = logical
   1

[the cyclist]

(I realized my mistake and deleted my comment before I saw you replied!)