Question 21
For $$n\in\mathbb{N}$$, consider non-negative integer-valued functions $$f$$ on $$\{1,2,..., n\}$$ satisfying $$f(i)\ge f(j)$$ for $$i>j$$ and $$\sum_{i=1}^{n}(i+f(i))=2023$$. Choose $$n$$ such that $$\sum_{i=1}^{n}f(i)$$ is the least. How many such functions exist in that case?
Correct Answer: 15
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