Omni-MATH / Find all natural numbers n(n≥2) such that there exists reals a₁,a₂,…,a_(n) which satisfy {|a_(i)−a_(j)|∣1≤i<j≤n}={1,2,…,(n(n−1))/(2)}. Let A={1,2,3,4,5,6},B={7,8,9,…,n}. …

Find all natural numbers n(n≥2) such that there exists reals a₁,a₂,…,a_(n) which satisfy {|a_(i)−a_(j)|∣1≤i<j≤n}={1,2,…,(n(n−1))/(2)}.

Let A={1,2,3,4,5,6},B={7,8,9,…,n}. A_(i)(i=1,2,…,20) contains eight numbers, three of which are chosen from A and the other five numbers from B. |A_(i)∩A_(j)|≤2,1≤i<j≤20. Find the minimum possible value of n.

Find all natural numbers $n (n \geq 2)$ such that there exists reals $a_1, a_2, \dots, a_n$ which satisfy \[ \{ |a_i - a_j| \mid 1\leq i<j \leq n\} = \left\{1,2,\dots,\frac{n(n-1)}{2}\right\}. \]

Let $A=\{1,2,3,4,5,6\}, B=\{7,8,9,\dots,n\}$. $A_i(i=1,2,\dots,20)$ contains eight numbers, three of which are chosen from $A$ and the other five numbers from $B$. $|A_i \cap A_j|\leq 2, 1\leq i<j\leq 20$. Find the minimum possible value of $n$.