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Omni-MATH / For any integer n≥2, let N(n) be the maxima number of triples (a_(i),b_(i),c_(i)), i=1,…,N(n), consisting of nonnegative integers a_(i), b_(i) and c_(i) such that the following two…

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problem

For any integer n≥2n\geq 2, let N(n)N(n) be the maxima number of triples (ai,bi,ci)(a_i, b_i, c_i), i=1,…,N(n)i=1, \ldots, N(n), consisting of nonnegative integers aia_i, bib_i and cic_i such that the following two conditions are satisfied: [list][*] ai+bi+ci=na_i+b_i+c_i=n for all i=1,…,N(n)i=1, \ldots, N(n), [*] If i≠ji\neq j then ai≠aja_i\neq a_j, bi≠bjb_i\neq b_j and ci≠cjc_i\neq c_j[/list] Determine N(n)N(n) for all n≥2n\geq 2. [i]
Plain-text mathematical notation (without MathML)
For any integer n≥2, let N(n) be the maxima number of triples (a_(i),b_(i),c_(i)), i=1,…,N(n), consisting of nonnegative integers a_(i), b_(i) and c_(i) such  that the following two conditions are satisfied:
[list][*] a_(i)+b_(i)+c_(i)=n for all i=1,…,N(n),
[*] If i≠j then a_(i)≠a_(j), b_(i)≠b_(j) and c_(i)≠c_(j)[/list]
Determine N(n) for all n≥2.

[i]
Original LaTeX notation
For any integer $n\geq 2$, let $N(n)$ be the maxima number of triples $(a_i, b_i, c_i)$, $i=1, \ldots, N(n)$, consisting of nonnegative integers $a_i$, $b_i$ and $c_i$ such  that the following two conditions are satisfied:
[list][*] $a_i+b_i+c_i=n$ for all $i=1, \ldots, N(n)$,
[*] If $i\neq j$ then $a_i\neq a_j$, $b_i\neq b_j$ and $c_i\neq c_j$[/list]
Determine $N(n)$ for all $n\geq 2$.

[i]

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Source and history

task_id
33e9f412-92a5-5fcd-be03-d04646c2e50f
task_key
test--33e9f412-92a5-5fcd-be03-d04646c2e50f
task_revision_id
1
config / split
/ test

Official source

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