Find the maximum number of pieces a rod can be cut

Here is the complete problem statement:

Given a rope of length n, you need to find the maximum number of pieces
you can make such that the length of every piece is in set {a, b, c} for
the given three values a, b, c

I know that the optimal solution can be achieved through Dynamic Programming, however, I have not learned that topic yet and I need to solve this problem recursively. With recursion, the main thing is to identify a subproblem and that's what I'm mainly having difficulty with doing. Can anyone give me an intuitive way to think of this problem? Sort of like a higher level description of the recursion if that makes sense. Is there an easier problem similar to this that I can try first that would help me solve this?

Thanks in advance.

It's already quite simple, with recursion we can just check all posibilities, in one step we can either cut away a piece of length a, b, or c so from problem of size n we get sup-problem of smaller size n-x

Of course we need a base case, so when n=0 we have succeeded so we can return 0, in case of n < 0 we have failed so we can return some negative infinity constant

Sample pseudo-code:

int solve(int n){
    if(n < 0) return -123456789; //-Infinity
    if(n == 0) return 0;
    return 1 + max(solve(n-a), solve(n-b), solve(n-c));
}

going to dynamic programming is as simple as setting up memo lookup table

int solve(int n){
    if(n < 0) return -123456789; //-Infinity
    if(n == 0) return 0;
    if(n in memo)return memo[n]
    return memo[n] = 1 + max(solve(n-a), solve(n-b), solve(n-c));
}