Find, for all large $n$, a non-trivial pairwise balanced block design $A_1,\dots ,A_m\subseteq \{1,\dots ,n\}$ such that, for all $t$, there are $O(n^{1/2})$ many $i$ such that $|A_i|=t$.

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Fix a large $n$ and write [ k:=\left\lceil \sqrt n\right\rceil,\qquad K:={k,k+1,\dots,2k-1}. ]

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.