Consider the following pseudocode where $n$ is a positive integer:\n\n``\ncount = 0\nfor i = 1 to n\n for j = i to n\n if (i + j) mod 3 = 0\n count = count + 1\n```\n\nFor $n = 12$, what is the value of $count$? Also give a closed‑form expression for $count$ as a function of $n$.

Question

Consider the following pseudocode where $n$ is a positive integer:\n\n``\ncount = 0\nfor i = 1 to n\n    for j = i to n\n        if (i + j) mod 3 = 0\n            count = count + 1\n```\n\nFor $n = 12$, what is the value of $count$? Also give a closed‑form expression for $count$ as a function of $n$.

Accepted Answer

26; count = a(a+1)/2 + b·c where a,b,c are the numbers of residues 0,1,2 modulo 3 respectively (see solution for piecewise formula).

Neco 2024 Computer Studies Question 18

Consider the following pseudocode where \(n\) is a positive integer:\n\n``\ncount = 0\nfor i = 1 to n\n for j = i to n\n if (i + j) mod 3 = 0\n count = count + 1\n```\n\nFor \(n = 12\), what is the value of \(count\)? Also give a closed‑form expression for \(count\) as a function of \(n\).

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