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Omni-MATH / For each interger n≥4, we consider the m subsets A₁,A₂,…,A_(m) of {1,2,3,…,n}, such that A₁ has exactly one element, A₂ has exactly two elements,...., A_(m) has exactly m elements …

Problem

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problem

For each interger n≥4n\geq 4, we consider the mm subsets A1,A2,…,AmA_1, A_2,\dots, A_m of {1,2,3,…,n}\{1, 2, 3,\dots, n\}, such that A1A_1 has exactly one element, A2A_2 has exactly two elements,...., AmA_m has exactly mm elements and none of these subsets is contained in any other set. Find the maximum value of mm.
Plain-text mathematical notation (without MathML)
For each interger n≥4, we consider the m subsets A₁,A₂,…,A_(m) of {1,2,3,…,n}, such that
A₁ has exactly one element, A₂ has exactly two elements,...., A_(m) has exactly m elements and none of these subsets is contained in any other set. Find the maximum value of m.
Original LaTeX notation
For each interger $n\geq 4$, we consider the $m$ subsets $A_1, A_2,\dots, A_m$ of $\{1, 2, 3,\dots, n\}$, such that
$A_1$ has exactly one element, $A_2$ has exactly two elements,...., $A_m$ has exactly $m$ elements and none of these subsets is contained in any other set. Find the maximum value of $m$.

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Source and history

task_id
f758e099-0bd6-5ad9-8064-77d9d3dcdc1f
task_key
test--f758e099-0bd6-5ad9-8064-77d9d3dcdc1f
task_revision_id
1
config / split
/ test

Official source

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