- I want to solve the equation:
$$ x_1 + x_2 +...+ x_n = s \\ \text{where }\ 0 < x_i \le c $$ - Or to rephrase the question count number of ways to break number $s$ in to $n$ numbers where each number is between $1$ to $c$.
- Without upper bound $x_i < c$ I can use stars and bars method. But since i have upper limit can i still use same method with some modification? Or can you reference me to some other method which can help me solve this.
2026-03-27 01:00:07.1774573207
How to count number of positive solutions of an equation $x_1 + x_2 +...+ x_n = s$ where $0 < x_i \le c $.
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