For n ∈ ℕ , consider non-negative integer-valued functions f on \ 1,2, , n\ satisfying f(i) ≥ f(j) for ij and ∑_ i=1 ^n(i+f(i))=2023 . Choose n such that ∑_ i=1 ^n f(i) is the least. How many such functions exist in

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For n ∈ ℕ , consider non-negative integer-valued functions f on \ 1,2, , n\ satisfying f(i) ≥ f(j) for i>j and ∑_ i=1 ^n(i+f(i))=2023 . Choose n such that ∑_ i=1 ^n f(i) is the least. How many such functions exist in

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Correct answer: 15

aligned & ∑_ i=1 ^n(i+f(i))=2023 & ∑_ i=1 ^n f(i)=2023-(n(n+1))/(2) aligned For ∑_ i=1 ^n f(i) be least, n=63 ∑_ i=1 ^n f(i) least =7 Total number of possible functions equal to number of possible partitions of 7. i.e. 7=1+1+1+1+1+1+1 =1+1+2+3 Total number of partitions =15 Number of possible functions =15

For n ∈ ℕ , consider non-negative integer-valued functions f on \...

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