Question 21
For every integer $n \ge 4$, consider $m$ subsets $A_1, A_2, A_3, \dots, A_m$ of $\{1, 2, 3, \dots, n\}$ such that:
* $A_1$ has $1$ element,
* $A_2$ has $2$ elements,
* $\dots$
* $A_m$ has $m$ elements,
and none of these subsets is contained in another. Find the maximum possible value of $m$.
* $A_1$ has $1$ element,
* $A_2$ has $2$ elements,
* $\dots$
* $A_m$ has $m$ elements,
and none of these subsets is contained in another. Find the maximum possible value of $m$.