Erdős Problem 665

### What is the conjecture

https://www.erdosproblems.com/665

A pairwise balanced design for $\\{1,\ldots,n\\}$ is a collection of sets $A_1,\ldots,A_m\subseteq \{1,\ldots,n\}$ such that $2\leq \lvert A_i\rvert 0$ and, for all large $n$, a pairwise balanced design such that $$\lvert A_i\rvert > n^{1/2}-C$$ for all $1\leq i\leq m$?

Status: open

### Choose either option
- [ ] I plan on working on this conjecture
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start with the conjecture statement and the linked Erdős Problems page, then inspect existing formalized conjectures in the repository to find the relevant entry point. Done means the pairwise balanced design conjecture is stated in Lean and the repository's checks pass.

Written by the indexing model from the issue text.